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[[618,48,24]] d ≤
n
618
k
48
d
24
kd²/n
44.7379
w
11
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 24, d_Z ≤ 24 · w_X = 11, w_Z = 11 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 24 · witness weight 24 (claimed upper_bound)
witness operator (support, 24 qubits)
[6, 7, 54, 55, 156, 157, 174, 175, 240, 241, 306, 307, 324, 325, 336, 337, 342, 343, 414, 415, 474, 475, 492, 493]
d_Z 24 · witness weight 24 (claimed upper_bound)
witness operator (support, 24 qubits)
[54, 55, 66, 67, 102, 103, 114, 115, 144, 145, 180, 181, 336, 337, 402, 403, 420, 421, 432, 433, 444, 445, 462, 463]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8–11 (mean 10.815) · H_Z 9–11 (mean 10.815)
qubit degrees H_X 4–10 (mean 5.67) · H_Z 3–10 (mean 5.67)
trapping sets H_X (1,4)×54 (2,5)×30 (3,6)×102 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 54 (1,5): 252 (1,6): 273 (1,10): 39 (2,5): 30 (2,6): 489 (2,7): 1284 (2,8): 3330 (2,9): 4248 (2,10): 3237 (2,12): 234 (2,13): 1080 (2,14): 1059 (2,16): 167 (2,18): 235 (3,6): 102 (3,7): 816 (3,8): 4935 (3,9): 16878 (3,10): 42300 (3,11): 74088 (3,12): 108405 (3,13): 106212 (3,14): 63354 (3,15): 22092 (3,16): 40473 (3,17): 51888 (3,18): 32388 (3,19): 7680 (3,20): 13214 (3,21): 12648 (3,22): 13533 (3,23): 654 (3,24): 2565 (3,26): 1302
trapping sets H_Z (1,3)×6 (2,4)×21 (3,5)×42 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 6 (1,4): 30 (1,5): 282 (1,6): 261 (1,10): 39 (2,4): 21 (2,5): 42 (2,6): 435 (2,7): 1146 (2,8): 3423 (2,9): 4542 (2,10): 3015 (2,11): 30 (2,12): 120 (2,13): 1218 (2,14): 1005 (2,16): 168 (2,18): 234 (3,5): 42 (3,6): 138 (3,7): 1160 (3,8): 4515 (3,9): 16296 (3,10): 39322 (3,11): 76824 (3,12): 110847 (3,13): 109480 (3,14): 59529 (3,15): 20070 (3,16): 40508 (3,17): 55488 (3,18): 29754 (3,19): 8928 (3,20): 11400 (3,21): 14322 (3,22): 12757 (3,23): 738 (3,24): 2543 (3,26): 1296

Construction & provenance

authors @TimoKellerMath
provenance submitted through the challenge
novelty novelty not audited
construction One [[6,4,2]] distance-amplification step (Liang, Gu, Chen, Eisert, Wang, arXiv:2609.37231, Eqs. (14), (15); amplifier checks G_X = G_Z = the all-one row of length 6) applied to the board entry codes/90-12-12.json ([[90,12,12]] two-block code over a group of order 45; d_X = d_Z = 12 certified in certs/90-12-12.json), keeping all of its checks.X except the rows [2, 12, 17, 31, 32, 44] and all of its checks.Z except the rows [14, 30, 34, 35, 42, 43] (linearly independent, 39 and 39 rows). Qubits: central (q,a) -> 6q+a (q a base qubit, 0 <= a < 6); t_j -> 540+j for the j-th kept Z-check z_j; s_i -> 579+i for the i-th kept X-check c_i. X-checks: (c_i,a) = {6q+a : q in c_i} + {s_i} (i, then a), then (q) = {6q,...,6q+5} + {t_j : q in z_j} (q = 0..89); Z-checks: (z_j,a) = {6q+a : q in z_j} + {t_j}, then (q) = {6q,...,6q+5} + {s_i : q in c_i}. n = 6*90 + 39 + 39 = 618 = 7n - k of the base, k = 4*12 = 48, check weight 11.
model Claude Claude Opus 5.5 (claimed, not verified)
builds on arXiv:2609.37231, arXiv:1512.07081, arXiv:2611.08247
date 2026-11-10
notes Distance: d_X = d_Z = 24 exactly: d_P = 2 d_P(base) for P = X, Z by Lemma 4 of arXiv:2609.37231 (proof in the coordinates of this entry: Proposition 4 of amplified-and-folded-codes/README.md, github.com/TimoKellerMath/quantum-error-correction @ c203901854da), and d_X = d_Z = 12 for the base is certified in certs/90-12-12.json (tropidist b03ec2d4077f, level solver). Witnesses: u (x) (e_0 + e_1) for the witnesses u of codes/90-12-12.json. Filed as upper_bound with these witnesses: the board earns the exact tier only through certs/, and its certifiers do not reach d = 24 at k = 48. The construction and the base are published; at board commit 8042f9da no CSS entry dominates or equals this code in (n, k, d, w), and no entry has its n and k unless named here; checked, not equivalent to an existing entry.
family distance-amplified (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight > 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[618,48,24]]: [[6,4,2]] amplification of 90-12-12

Direction & hypothesis

Cell: check weight 11, so the any weight class, unrestricted locality (no layout submitted), CSS board. One step of the distance amplification of Liang, Gu, Chen, Eisert and Wang (arXiv:2609.37231) with the [[N,N-2,2]] amplifier turns a CSS code [[n,k,d]] whose retained checks are linearly independent into a [[(N+1)n - k, (N-2)k, 2d]] code, at check weight max(w_X + 1, w_Z + 1, N + q_Z, N + q_X) with q the largest column weights. The distance doubles exactly, for X and Z separately (Lemma 4 there), so every board base with a certified exact distance gives an amplified code with a proved exact distance. Hypothesis: some of these are new points of the frontier, in particular where the board's amplified entries keep dependent base rows (which only lengthen the code) or use bases without a certificate. Here the base is codes/90-12-12.json ([[90,12,12]] two-block code over a group of order 45, board entry of @FarLab), certified exact in certs/90-12-12.json.

What was searched

All CSS entries of board commit 8042f9da with an exact certificate were amplified on paper with the [[N,N-2,2]] amplifiers for N = 4, 6, 8, 10 (935, 784, 664 and 567 bases with (N+1)n - k <= 1000). Of the admissible candidates with check weight at most 12, 89 are not dominated by a CSS entry in (n, k, d, w) and 57 of these also not by each other; most have d = 4 (high-rate bases of distance 2). The eight with d >= 12 were built and verified, with linearly independent base rows spanning the row spaces chosen to minimize the check weight (randomized greedy; a counting bound shows that no choice of rows gives a lower weight). This code is one of them.

Evidence trail

  • Construction: Definition 1 of the README of the package cited below, with the base rows listed in provenance.construction left out (39 of 45 X-checks and 39 of 45 Z-checks kept); n = 618 = 7 x 90 - 12, k = 48 by GF(2) ranks, check weight 11, qubit degree at most 16 (10 X-checks, 10 Z-checks).
  • Distance (proved): d_X = 2 d_X(base) = 24 and d_Z = 2 d_Z(base) = 24 by Lemma 4 of arXiv:2609.37231 (written out in the coordinates of this entry as Proposition 4 of the README), since d_X(base) = d_Z(base) = 12 is certified in certs/90-12-12.json (tropidist b03ec2d4077f, level solver). Witnesses: u (x) (e_0 + e_1) for the witnesses u of codes/90-12-12.json.
  • Consistency check (computed, heuristic): an information-set search with 1.1e5 trials per side found nothing lighter than 24; the 9008 and 8781 distinct words of weight 24 it found (X, Z) all have the form l (x) (e_a + e_b) with l a weight-12 logical of the base, as the proof predicts (Lemma 5 of the README; with the 2685 such logicals of the base found by a saturated search there are 15 x 2685 = 40275 of them per side).
  • Board placement (computed at 8042f9da): no CSS entry dominates or equals it in (n, k, d, w); it dominates no entry, so it is a new point of the frontier.
  • Final claim: d = 24 exactly, by proof. Filed as upper_bound with the witnesses, since the board earns the exact tier only through certs/ and its certifiers do not reach d = 24 at k = 48.

Dead ends

  • Most amplifications of certified bases are on the board already or dominated: by our audit, 70 of the 80 amplified entries of 8042f9da are amplifications of certified bases (so their distances are exact by the same lemma), and for example [[90,8,10]] and [[108,8,10]] give [[442,16,20]] and [[532,16,20]] at check weight 7, dominated by the board's [[252,16,d<=20]].
  • The [[4,2,2]] step costs more than one unit of check weight when a column weight of the base exceeds w - 3: [[48,4,7]] and [[60,4,8]] (w = 5, column weight 3) give [[236,8,14]] and [[296,8,16]] at check weight 7, dominated by [[140,8,14]] and [[180,12,d<=16]].

Tools

Claude Opus 5.5 (Claude Code); Python (standard library) for the construction, ranks and checks; an information-set search in C; tropidist (Cheng, Guo, Pan, arXiv:2611.08247) at the board's pinned commit b03ec2d4077f for the direct runs. The verification of all eight amplified codes took about 45 CPU-minutes.

Reproduction

In amplified-and-folded-codes/ of github.com/TimoKellerMath/quantum-error-correction @ c203901854da, python3 src/rebuild.py rebuilds the check matrices of this entry from a copy of codes/90-12-12.json and the list of dropped rows (data/codes/618-48-24.json), compares them row by row and checks n, k, the weights, the CSS condition and both witnesses; README.md there contains the definitions and the proofs.

Parity checks

X-checks 324 (max weight 11) · Z-checks 324 (max weight 11)
H_X (324 checks, sparse supports)
[0, 24, 126, 162, 258, 270, 306, 420, 462, 492, 579] [1, 25, 127, 163, 259, 271, 307, 421, 463, 493, 579] [2, 26, 128, 164, 260, 272, 308, 422, 464, 494, 579] [3, 27, 129, 165, 261, 273, 309, 423, 465, 495, 579] [4, 28, 130, 166, 262, 274, 310, 424, 466, 496, 579] [5, 29, 131, 167, 263, 275, 311, 425, 467, 497, 579] [6, 30, 132, 168, 264, 276, 312, 426, 450, 498, 580] [7, 31, 133, 169, 265, 277, 313, 427, 451, 499, 580] [8, 32, 134, 170, 266, 278, 314, 428, 452, 500, 580] [9, 33, 135, 171, 267, 279, 315, 429, 453, 501, 580] [10, 34, 136, 172, 268, 280, 316, 430, 454, 502, 580] [11, 35, 137, 173, 269, 281, 317, 431, 455, 503, 580] [18, 42, 144, 180, 222, 270, 288, 384, 480, 510, 581] [19, 43, 145, 181, 223, 271, 289, 385, 481, 511, 581] [20, 44, 146, 182, 224, 272, 290, 386, 482, 512, 581] [21, 45, 147, 183, 225, 273, 291, 387, 483, 513, 581] [22, 46, 148, 184, 226, 274, 292, 388, 484, 514, 581] [23, 47, 149, 185, 227, 275, 293, 389, 485, 515, 581] [24, 48, 150, 186, 228, 276, 294, 390, 468, 516, 582] [25, 49, 151, 187, 229, 277, 295, 391, 469, 517, 582] [26, 50, 152, 188, 230, 278, 296, 392, 470, 518, 582] [27, 51, 153, 189, 231, 279, 297, 393, 471, 519, 582] [28, 52, 154, 190, 232, 280, 298, 394, 472, 520, 582] [29, 53, 155, 191, 233, 281, 299, 395, 473, 521, 582] [30, 36, 156, 192, 216, 282, 300, 378, 474, 504, 583] [31, 37, 157, 193, 217, 283, 301, 379, 475, 505, 583] [32, 38, 158, 194, 218, 284, 302, 380, 476, 506, 583] [33, 39, 159, 195, 219, 285, 303, 381, 477, 507, 583] [34, 40, 160, 196, 220, 286, 304, 382, 478, 508, 583] [35, 41, 161, 197, 221, 287, 305, 383, 479, 509, 583] [6, 36, 108, 198, 240, 288, 306, 402, 444, 528, 584] [7, 37, 109, 199, 241, 289, 307, 403, 445, 529, 584] [8, 38, 110, 200, 242, 290, 308, 404, 446, 530, 584] [9, 39, 111, 201, 243, 291, 309, 405, 447, 531, 584] [10, 40, 112, 202, 244, 292, 310, 406, 448, 532, 584] [11, 41, 113, 203, 245, 293, 311, 407, 449, 533, 584] [12, 42, 114, 204, 246, 294, 312, 408, 432, 534, 585] [13, 43, 115, 205, 247, 295, 313, 409, 433, 535, 585] [14, 44, 116, 206, 248, 296, 314, 410, 434, 536, 585] [15, 45, 117, 207, 249, 297, 315, 411, 435, 537, 585] [16, 46, 118, 208, 250, 298, 316, 412, 436, 538, 585] [17, 47, 119, 209, 251, 299, 317, 413, 437, 539, 585] [0, 48, 120, 210, 234, 300, 318, 396, 438, 522, 586] [1, 49, 121, 211, 235, 301, 319, 397, 439, 523, 586] [2, 50, 122, 212, 236, 302, 320, 398, 440, 524, 586] [3, 51, 123, 213, 237, 303, 321, 399, 441, 525, 586] [4, 52, 124, 214, 238, 304, 322, 400, 442, 526, 586] [5, 53, 125, 215, 239, 305, 323, 401, 443, 527, 586] [42, 54, 78, 180, 216, 276, 324, 360, 474, 516, 587] [43, 55, 79, 181, 217, 277, 325, 361, 475, 517, 587] [44, 56, 80, 182, 218, 278, 326, 362, 476, 518, 587] [45, 57, 81, 183, 219, 279, 327, 363, 477, 519, 587] [46, 58, 82, 184, 220, 280, 328, 364, 478, 520, 587] [47, 59, 83, 185, 221, 281, 329, 365, 479, 521, 587] [48, 60, 84, 186, 222, 282, 330, 366, 480, 504, 588] [49, 61, 85, 187, 223, 283, 331, 367, 481, 505, 588] [50, 62, 86, 188, 224, 284, 332, 368, 482, 506, 588] [51, 63, 87, 189, 225, 285, 333, 369, 483, 507, 588] [52, 64, 88, 190, 226, 286, 334, 370, 484, 508, 588] [53, 65, 89, 191, 227, 287, 335, 371, 485, 509, 588] [36, 66, 72, 192, 228, 270, 336, 372, 468, 510, 589] [37, 67, 73, 193, 229, 271, 337, 373, 469, 511, 589] [38, 68, 74, 194, 230, 272, 338, 374, 470, 512, 589] [39, 69, 75, 195, 231, 273, 339, 375, 471, 513, 589] [40, 70, 76, 196, 232, 274, 340, 376, 472, 514, 589] [41, 71, 77, 197, 233, 275, 341, 377, 473, 515, 589] [12, 78, 102, 204, 240, 300, 330, 348, 444, 522, 590] [13, 79, 103, 205, 241, 301, 331, 349, 445, 523, 590] [14, 80, 104, 206, 242, 302, 332, 350, 446, 524, 590] [15, 81, 105, 207, 243, 303, 333, 351, 447, 525, 590] [16, 82, 106, 208, 244, 304, 334, 352, 448, 526, 590] [17, 83, 107, 209, 245, 305, 335, 353, 449, 527, 590] [0, 84, 90, 210, 246, 288, 336, 354, 432, 528, 591] [1, 85, 91, 211, 247, 289, 337, 355, 433, 529, 591] [2, 86, 92, 212, 248, 290, 338, 356, 434, 530, 591] [3, 87, 93, 213, 249, 291, 339, 357, 435, 531, 591] [4, 88, 94, 214, 250, 292, 340, 358, 436, 532, 591] [5, 89, 95, 215, 251, 293, 341, 359, 437, 533, 591] [24, 60, 90, 162, 252, 312, 342, 360, 456, 498, 592] [25, 61, 91, 163, 253, 313, 343, 361, 457, 499, 592] [26, 62, 92, 164, 254, 314, 344, 362, 458, 500, 592] [27, 63, 93, 165, 255, 315, 345, 363, 459, 501, 592] [28, 64, 94, 166, 256, 316, 346, 364, 460, 502, 592] [29, 65, 95, 167, 257, 317, 347, 365, 461, 503, 592] [30, 66, 96, 168, 258, 318, 348, 366, 462, 486, 593] [31, 67, 97, 169, 259, 319, 349, 367, 463, 487, 593] [32, 68, 98, 170, 260, 320, 350, 368, 464, 488, 593] [33, 69, 99, 171, 261, 321, 351, 369, 465, 489, 593] [34, 70, 100, 172, 262, 322, 352, 370, 466, 490, 593] [35, 71, 101, 173, 263, 323, 353, 371, 467, 491, 593] [0, 96, 108, 132, 234, 300, 330, 378, 414, 528, 594] [1, 97, 109, 133, 235, 301, 331, 379, 415, 529, 594] [2, 98, 110, 134, 236, 302, 332, 380, 416, 530, 594] [3, 99, 111, 135, 237, 303, 333, 381, 417, 531, 594] [4, 100, 112, 136, 238, 304, 334, 382, 418, 532, 594] [5, 101, 113, 137, 239, 305, 335, 383, 419, 533, 594] [6, 102, 114, 138, 240, 288, 336, 384, 420, 534, 595] [7, 103, 115, 139, 241, 289, 337, 385, 421, 535, 595] [8, 104, 116, 140, 242, 290, 338, 386, 422, 536, 595] [9, 105, 117, 141, 243, 291, 339, 387, 423, 537, 595] [10, 106, 118, 142, 244, 292, 340, 388, 424, 538, 595] [11, 107, 119, 143, 245, 293, 341, 389, 425, 539, 595] [12, 90, 120, 126, 246, 294, 324, 390, 426, 522, 596] [13, 91, 121, 127, 247, 295, 325, 391, 427, 523, 596] [14, 92, 122, 128, 248, 296, 326, 392, 428, 524, 596] [15, 93, 123, 129, 249, 297, 327, 393, 429, 525, 596] [16, 94, 124, 130, 250, 298, 328, 394, 430, 526, 596] [17, 95, 125, 131, 251, 299, 329, 395, 431, 527, 596] [18, 60, 126, 150, 252, 318, 348, 378, 396, 492, 597] [19, 61, 127, 151, 253, 319, 349, 379, 397, 493, 597] [20, 62, 128, 152, 254, 320, 350, 380, 398, 494, 597] [21, 63, 129, 153, 255, 321, 351, 381, 399, 495, 597] [22, 64, 130, 154, 256, 322, 352, 382, 400, 496, 597] [23, 65, 131, 155, 257, 323, 353, 383, 401, 497, 597] [24, 66, 132, 156, 258, 306, 354, 384, 402, 498, 598] [25, 67, 133, 157, 259, 307, 355, 385, 403, 499, 598] [26, 68, 134, 158, 260, 308, 356, 386, 404, 500, 598] [27, 69, 135, 159, 261, 309, 357, 387, 405, 501, 598] [28, 70, 136, 160, 262, 310, 358, 388, 406, 502, 598] [29, 71, 137, 161, 263, 311, 359, 389, 407, 503, 598] [30, 54, 138, 144, 264, 312, 342, 390, 408, 486, 599] [31, 55, 139, 145, 265, 313, 343, 391, 409, 487, 599] [32, 56, 140, 146, 266, 314, 344, 392, 410, 488, 599] [33, 57, 141, 147, 267, 315, 345, 393, 411, 489, 599] [34, 58, 142, 148, 268, 316, 346, 394, 412, 490, 599] [35, 59, 143, 149, 269, 317, 347, 395, 413, 491, 599] [36, 78, 114, 144, 216, 282, 366, 396, 414, 510, 600] [37, 79, 115, 145, 217, 283, 367, 397, 415, 511, 600] [38, 80, 116, 146, 218, 284, 368, 398, 416, 512, 600] [39, 81, 117, 147, 219, 285, 369, 399, 417, 513, 600] [40, 82, 118, 148, 220, 286, 370, 400, 418, 514, 600] [41, 83, 119, 149, 221, 287, 371, 401, 419, 515, 600] [42, 84, 120, 150, 222, 270, 372, 402, 420, 516, 601] [43, 85, 121, 151, 223, 271, 373, 403, 421, 517, 601] [44, 86, 122, 152, 224, 272, 374, 404, 422, 518, 601] [45, 87, 123, 153, 225, 273, 375, 405, 423, 519, 601] [46, 88, 124, 154, 226, 274, 376, 406, 424, 520, 601] [47, 89, 125, 155, 227, 275, 377, 407, 425, 521, 601] [48, 72, 108, 156, 228, 276, 360, 408, 426, 504, 602] [49, 73, 109, 157, 229, 277, 361, 409, 427, 505, 602] [50, 74, 110, 158, 230, 278, 362, 410, 428, 506, 602] [51, 75, 111, 159, 231, 279, 363, 411, 429, 507, 602] [52, 76, 112, 160, 232, 280, 364, 412, 430, 508, 602] [53, 77, 113, 161, 233, 281, 365, 413, 431, 509, 602] [18, 54, 150, 162, 186, 312, 354, 384, 432, 468, 603] [19, 55, 151, 163, 187, 313, 355, 385, 433, 469, 603] [20, 56, 152, 164, 188, 314, 356, 386, 434, 470, 603] [21, 57, 153, 165, 189, 315, 357, 387, 435, 471, 603] [22, 58, 154, 166, 190, 316, 358, 388, 436, 472, 603] [23, 59, 155, 167, 191, 317, 359, 389, 437, 473, 603] [24, 60, 156, 168, 192, 318, 342, 390, 438, 474, 604] [25, 61, 157, 169, 193, 319, 343, 391, 439, 475, 604] [26, 62, 158, 170, 194, 320, 344, 392, 440, 476, 604] [27, 63, 159, 171, 195, 321, 345, 393, 441, 477, 604] [28, 64, 160, 172, 196, 322, 346, 394, 442, 478, 604] [29, 65, 161, 173, 197, 323, 347, 395, 443, 479, 604] [30, 66, 144, 174, 180, 306, 348, 378, 444, 480, 605] [31, 67, 145, 175, 181, 307, 349, 379, 445, 481, 605] [32, 68, 146, 176, 182, 308, 350, 380, 446, 482, 605] [33, 69, 147, 177, 183, 309, 351, 381, 447, 483, 605] [34, 70, 148, 178, 184, 310, 352, 382, 448, 484, 605] [35, 71, 149, 179, 185, 311, 353, 383, 449, 485, 605] [36, 72, 114, 180, 204, 276, 372, 402, 432, 450, 606] [37, 73, 115, 181, 205, 277, 373, 403, 433, 451, 606] [38, 74, 116, 182, 206, 278, 374, 404, 434, 452, 606] [39, 75, 117, 183, 207, 279, 375, 405, 435, 453, 606] [40, 76, 118, 184, 208, 280, 376, 406, 436, 454, 606] [41, 77, 119, 185, 209, 281, 377, 407, 437, 455, 606] [0, 90, 132, 168, 198, 294, 336, 420, 450, 468, 607] [1, 91, 133, 169, 199, 295, 337, 421, 451, 469, 607] [2, 92, 134, 170, 200, 296, 338, 422, 452, 470, 607] [3, 93, 135, 171, 201, 297, 339, 423, 453, 471, 607] [4, 94, 136, 172, 202, 298, 340, 424, 454, 472, 607] [5, 95, 137, 173, 203, 299, 341, 425, 455, 473, 607] [6, 96, 138, 174, 204, 300, 324, 426, 456, 474, 608] [7, 97, 139, 175, 205, 301, 325, 427, 457, 475, 608] [8, 98, 140, 176, 206, 302, 326, 428, 458, 476, 608] [9, 99, 141, 177, 207, 303, 327, 429, 459, 477, 608] [10, 100, 142, 178, 208, 304, 328, 430, 460, 478, 608] [11, 101, 143, 179, 209, 305, 329, 431, 461, 479, 608] [12, 102, 126, 162, 210, 288, 330, 414, 462, 480, 609] [13, 103, 127, 163, 211, 289, 331, 415, 463, 481, 609] [14, 104, 128, 164, 212, 290, 332, 416, 464, 482, 609] [15, 105, 129, 165, 213, 291, 333, 417, 465, 483, 609] [16, 106, 130, 166, 214, 292, 334, 418, 466, 484, 609] [17, 107, 131, 167, 215, 293, 335, 419, 467, 485, 609] [72, 108, 204, 216, 240, 366, 408, 438, 486, 522, 610] [73, 109, 205, 217, 241, 367, 409, 439, 487, 523, 610] [74, 110, 206, 218, 242, 368, 410, 440, 488, 524, 610] [75, 111, 207, 219, 243, 369, 411, 441, 489, 525, 610] [76, 112, 208, 220, 244, 370, 412, 442, 490, 526, 610] [77, 113, 209, 221, 245, 371, 413, 443, 491, 527, 610] [78, 114, 210, 222, 246, 372, 396, 444, 492, 528, 611] [79, 115, 211, 223, 247, 373, 397, 445, 493, 529, 611] [80, 116, 212, 224, 248, 374, 398, 446, 494, 530, 611] [81, 117, 213, 225, 249, 375, 399, 447, 495, 531, 611] [82, 118, 214, 226, 250, 376, 400, 448, 496, 532, 611] [83, 119, 215, 227, 251, 377, 401, 449, 497, 533, 611] [84, 120, 198, 228, 234, 360, 402, 432, 498, 534, 612] [85, 121, 199, 229, 235, 361, 403, 433, 499, 535, 612] [86, 122, 200, 230, 236, 362, 404, 434, 500, 536, 612] [87, 123, 201, 231, 237, 363, 405, 435, 501, 537, 612] [88, 124, 202, 232, 238, 364, 406, 436, 502, 538, 612] [89, 125, 203, 233, 239, 365, 407, 437, 503, 539, 612] [90, 126, 168, 234, 258, 330, 426, 456, 486, 504, 613] [91, 127, 169, 235, 259, 331, 427, 457, 487, 505, 613] [92, 128, 170, 236, 260, 332, 428, 458, 488, 506, 613] [93, 129, 171, 237, 261, 333, 429, 459, 489, 507, 613] [94, 130, 172, 238, 262, 334, 430, 460, 490, 508, 613] [95, 131, 173, 239, 263, 335, 431, 461, 491, 509, 613] [96, 132, 174, 240, 264, 336, 414, 462, 492, 510, 614] [97, 133, 175, 241, 265, 337, 415, 463, 493, 511, 614] [98, 134, 176, 242, 266, 338, 416, 464, 494, 512, 614] [99, 135, 177, 243, 267, 339, 417, 465, 495, 513, 614] [100, 136, 178, 244, 268, 340, 418, 466, 496, 514, 614] [101, 137, 179, 245, 269, 341, 419, 467, 497, 515, 614] [102, 138, 162, 246, 252, 324, 420, 450, 498, 516, 615] [103, 139, 163, 247, 253, 325, 421, 451, 499, 517, 615] [104, 140, 164, 248, 254, 326, 422, 452, 500, 518, 615] [105, 141, 165, 249, 255, 327, 423, 453, 501, 519, 615] [106, 142, 166, 250, 256, 328, 424, 454, 502, 520, 615] [107, 143, 167, 251, 257, 329, 425, 455, 503, 521, 615] [54, 144, 186, 222, 252, 348, 390, 474, 504, 522, 616] [55, 145, 187, 223, 253, 349, 391, 475, 505, 523, 616] [56, 146, 188, 224, 254, 350, 392, 476, 506, 524, 616] [57, 147, 189, 225, 255, 351, 393, 477, 507, 525, 616] [58, 148, 190, 226, 256, 352, 394, 478, 508, 526, 616] [59, 149, 191, 227, 257, 353, 395, 479, 509, 527, 616] [60, 150, 192, 228, 258, 354, 378, 480, 510, 528, 617] [61, 151, 193, 229, 259, 355, 379, 481, 511, 529, 617] [62, 152, 194, 230, 260, 356, 380, 482, 512, 530, 617] [63, 153, 195, 231, 261, 357, 381, 483, 513, 531, 617] [64, 154, 196, 232, 262, 358, 382, 484, 514, 532, 617] [65, 155, 197, 233, 263, 359, 383, 485, 515, 533, 617] [0, 1, 2, 3, 4, 5, 540, 546, 564, 570, 573] [6, 7, 8, 9, 10, 11, 541, 547, 565, 574] [12, 13, 14, 15, 16, 17, 542, 548, 563, 569, 572] [18, 19, 20, 21, 22, 23, 540, 543, 558, 576] [24, 25, 26, 27, 28, 29, 541, 544, 559, 571, 577] [30, 31, 32, 33, 34, 35, 542, 545, 557, 575] [36, 37, 38, 39, 40, 41, 543, 546, 561, 568] [42, 43, 44, 45, 46, 47, 544, 547, 562, 566, 578] [48, 49, 50, 51, 52, 53, 545, 548, 560, 567] [54, 55, 56, 57, 58, 59, 541, 549, 554, 577] [60, 61, 62, 63, 64, 65, 542, 550, 555, 575] [66, 67, 68, 69, 70, 71, 540, 551, 556, 571, 576] [72, 73, 74, 75, 76, 77, 544, 549, 552, 567, 578] [78, 79, 80, 81, 82, 83, 545, 550, 553, 568] [84, 85, 86, 87, 88, 89, 543, 551, 566] [90, 91, 92, 93, 94, 95, 547, 552, 554, 569, 574] [96, 97, 98, 99, 100, 101, 548, 553, 555, 570, 572] [102, 103, 104, 105, 106, 107, 546, 556, 573] [108, 109, 110, 111, 112, 113, 545, 550, 557, 563] [114, 115, 116, 117, 118, 119, 543, 551, 558, 564, 578] [120, 121, 122, 123, 124, 125, 544, 549, 559, 565] [126, 127, 128, 129, 130, 131, 548, 553, 557, 560, 573] [132, 133, 134, 135, 136, 137, 546, 558, 561, 574] [138, 139, 140, 141, 142, 143, 547, 552, 559, 562, 572] [144, 145, 146, 147, 148, 149, 542, 555, 560, 563, 576] [150, 151, 152, 153, 154, 155, 540, 556, 561, 564, 577] [156, 157, 158, 159, 160, 161, 541, 554, 562, 565, 575] [162, 163, 164, 165, 166, 167, 547, 558, 566, 571] [168, 169, 170, 171, 172, 173, 548, 552, 559, 567] [174, 175, 176, 177, 178, 179, 546, 553, 557, 568] [180, 181, 182, 183, 184, 185, 541, 556, 561, 566] [186, 187, 188, 189, 190, 191, 542, 554, 562, 567, 569] [192, 193, 194, 195, 196, 197, 540, 555, 560, 568, 570] [198, 199, 200, 201, 202, 203, 544, 551, 564, 571] [204, 205, 206, 207, 208, 209, 545, 549, 565, 569] [210, 211, 212, 213, 214, 215, 543, 550, 563, 570] [216, 217, 218, 219, 220, 221, 555, 562, 567, 572] [222, 223, 224, 225, 226, 227, 556, 560, 568, 573] [228, 229, 230, 231, 232, 233, 554, 561, 566, 574, 578] [234, 235, 236, 237, 238, 239, 550, 565, 569, 572, 575] [240, 241, 242, 243, 244, 245, 551, 563, 570, 573, 576] [246, 247, 248, 249, 250, 251, 549, 564, 574, 577] [252, 253, 254, 255, 256, 257, 553, 559, 575] [258, 259, 260, 261, 262, 263, 557, 576] [264, 265, 266, 267, 268, 269, 552, 558, 571, 577, 578] [270, 271, 272, 273, 274, 275, 540, 544, 560, 566] [276, 277, 278, 279, 280, 281, 541, 545, 561, 567, 578] [282, 283, 284, 285, 286, 287, 542, 543, 562, 568] [288, 289, 290, 291, 292, 293, 543, 547, 563, 573] [294, 295, 296, 297, 298, 299, 544, 548, 564, 569, 574] [300, 301, 302, 303, 304, 305, 545, 546, 565, 570, 572] [306, 307, 308, 309, 310, 311, 541, 546, 557, 571, 576] [312, 313, 314, 315, 316, 317, 542, 547, 558, 577] [318, 319, 320, 321, 322, 323, 540, 548, 559, 575] [324, 325, 326, 327, 328, 329, 547, 549, 553, 572] [330, 331, 332, 333, 334, 335, 548, 550, 569, 573] [336, 337, 338, 339, 340, 341, 546, 551, 552, 570, 574] [342, 343, 344, 345, 346, 347, 541, 552, 555, 571, 575] [348, 349, 350, 351, 352, 353, 542, 553, 556, 576] [354, 355, 356, 357, 358, 359, 540, 554, 577] [360, 361, 362, 363, 364, 365, 544, 550, 554, 566] [366, 367, 368, 369, 370, 371, 545, 551, 555, 567] [372, 373, 374, 375, 376, 377, 543, 549, 556, 568, 578] [378, 379, 380, 381, 382, 383, 540, 555, 557, 561, 575] [384, 385, 386, 387, 388, 389, 541, 556, 558, 562, 576] [390, 391, 392, 393, 394, 395, 542, 554, 559, 560, 577] [396, 397, 398, 399, 400, 401, 543, 550, 560, 564] [402, 403, 404, 405, 406, 407, 544, 551, 561, 565] [408, 409, 410, 411, 412, 413, 545, 549, 562, 563, 578] [414, 415, 416, 417, 418, 419, 546, 553, 558, 563, 572] [420, 421, 422, 423, 424, 425, 547, 559, 564, 573] [426, 427, 428, 429, 430, 431, 548, 552, 557, 565, 574] [432, 433, 434, 435, 436, 437, 543, 549, 564, 566, 569] [438, 439, 440, 441, 442, 443, 544, 550, 565, 567, 570] [444, 445, 446, 447, 448, 449, 545, 551, 563, 568] [450, 451, 452, 453, 454, 455, 546, 552, 558] [456, 457, 458, 459, 460, 461, 547, 553, 559, 569] [462, 463, 464, 465, 466, 467, 548, 557, 570, 571] [468, 469, 470, 471, 472, 473, 540, 554, 561, 567, 571] [474, 475, 476, 477, 478, 479, 541, 555, 562, 568] [480, 481, 482, 483, 484, 485, 542, 556, 560, 566] [486, 487, 488, 489, 490, 491, 552, 557, 572, 576] [492, 493, 494, 495, 496, 497, 553, 558, 573, 577] [498, 499, 500, 501, 502, 503, 559, 571, 574, 575] [504, 505, 506, 507, 508, 509, 554, 560, 567, 575] [510, 511, 512, 513, 514, 515, 555, 561, 568, 576, 578] [516, 517, 518, 519, 520, 521, 556, 562, 566, 577] [522, 523, 524, 525, 526, 527, 549, 563, 569, 573] [528, 529, 530, 531, 532, 533, 550, 564, 570, 574] [534, 535, 536, 537, 538, 539, 551, 565, 572, 578]
H_Z (324 checks, sparse supports)
[0, 18, 66, 150, 192, 270, 318, 354, 378, 468, 540] [1, 19, 67, 151, 193, 271, 319, 355, 379, 469, 540] [2, 20, 68, 152, 194, 272, 320, 356, 380, 470, 540] [3, 21, 69, 153, 195, 273, 321, 357, 381, 471, 540] [4, 22, 70, 154, 196, 274, 322, 358, 382, 472, 540] [5, 23, 71, 155, 197, 275, 323, 359, 383, 473, 540] [6, 24, 54, 156, 180, 276, 306, 342, 384, 474, 541] [7, 25, 55, 157, 181, 277, 307, 343, 385, 475, 541] [8, 26, 56, 158, 182, 278, 308, 344, 386, 476, 541] [9, 27, 57, 159, 183, 279, 309, 345, 387, 477, 541] [10, 28, 58, 160, 184, 280, 310, 346, 388, 478, 541] [11, 29, 59, 161, 185, 281, 311, 347, 389, 479, 541] [12, 30, 60, 144, 186, 282, 312, 348, 390, 480, 542] [13, 31, 61, 145, 187, 283, 313, 349, 391, 481, 542] [14, 32, 62, 146, 188, 284, 314, 350, 392, 482, 542] [15, 33, 63, 147, 189, 285, 315, 351, 393, 483, 542] [16, 34, 64, 148, 190, 286, 316, 352, 394, 484, 542] [17, 35, 65, 149, 191, 287, 317, 353, 395, 485, 542] [18, 36, 84, 114, 210, 282, 288, 372, 396, 432, 543] [19, 37, 85, 115, 211, 283, 289, 373, 397, 433, 543] [20, 38, 86, 116, 212, 284, 290, 374, 398, 434, 543] [21, 39, 87, 117, 213, 285, 291, 375, 399, 435, 543] [22, 40, 88, 118, 214, 286, 292, 376, 400, 436, 543] [23, 41, 89, 119, 215, 287, 293, 377, 401, 437, 543] [24, 42, 72, 120, 198, 270, 294, 360, 402, 438, 544] [25, 43, 73, 121, 199, 271, 295, 361, 403, 439, 544] [26, 44, 74, 122, 200, 272, 296, 362, 404, 440, 544] [27, 45, 75, 123, 201, 273, 297, 363, 405, 441, 544] [28, 46, 76, 124, 202, 274, 298, 364, 406, 442, 544] [29, 47, 77, 125, 203, 275, 299, 365, 407, 443, 544] [30, 48, 78, 108, 204, 276, 300, 366, 408, 444, 545] [31, 49, 79, 109, 205, 277, 301, 367, 409, 445, 545] [32, 50, 80, 110, 206, 278, 302, 368, 410, 446, 545] [33, 51, 81, 111, 207, 279, 303, 369, 411, 447, 545] [34, 52, 82, 112, 208, 280, 304, 370, 412, 448, 545] [35, 53, 83, 113, 209, 281, 305, 371, 413, 449, 545] [0, 36, 102, 132, 174, 300, 306, 336, 414, 450, 546] [1, 37, 103, 133, 175, 301, 307, 337, 415, 451, 546] [2, 38, 104, 134, 176, 302, 308, 338, 416, 452, 546] [3, 39, 105, 135, 177, 303, 309, 339, 417, 453, 546] [4, 40, 106, 136, 178, 304, 310, 340, 418, 454, 546] [5, 41, 107, 137, 179, 305, 311, 341, 419, 455, 546] [6, 42, 90, 138, 162, 288, 312, 324, 420, 456, 547] [7, 43, 91, 139, 163, 289, 313, 325, 421, 457, 547] [8, 44, 92, 140, 164, 290, 314, 326, 422, 458, 547] [9, 45, 93, 141, 165, 291, 315, 327, 423, 459, 547] [10, 46, 94, 142, 166, 292, 316, 328, 424, 460, 547] [11, 47, 95, 143, 167, 293, 317, 329, 425, 461, 547] [12, 48, 96, 126, 168, 294, 318, 330, 426, 462, 548] [13, 49, 97, 127, 169, 295, 319, 331, 427, 463, 548] [14, 50, 98, 128, 170, 296, 320, 332, 428, 464, 548] [15, 51, 99, 129, 171, 297, 321, 333, 429, 465, 548] [16, 52, 100, 130, 172, 298, 322, 334, 430, 466, 548] [17, 53, 101, 131, 173, 299, 323, 335, 431, 467, 548] [54, 72, 120, 204, 246, 324, 372, 408, 432, 522, 549] [55, 73, 121, 205, 247, 325, 373, 409, 433, 523, 549] [56, 74, 122, 206, 248, 326, 374, 410, 434, 524, 549] [57, 75, 123, 207, 249, 327, 375, 411, 435, 525, 549] [58, 76, 124, 208, 250, 328, 376, 412, 436, 526, 549] [59, 77, 125, 209, 251, 329, 377, 413, 437, 527, 549] [60, 78, 108, 210, 234, 330, 360, 396, 438, 528, 550] [61, 79, 109, 211, 235, 331, 361, 397, 439, 529, 550] [62, 80, 110, 212, 236, 332, 362, 398, 440, 530, 550] [63, 81, 111, 213, 237, 333, 363, 399, 441, 531, 550] [64, 82, 112, 214, 238, 334, 364, 400, 442, 532, 550] [65, 83, 113, 215, 239, 335, 365, 401, 443, 533, 550] [66, 84, 114, 198, 240, 336, 366, 402, 444, 534, 551] [67, 85, 115, 199, 241, 337, 367, 403, 445, 535, 551] [68, 86, 116, 200, 242, 338, 368, 404, 446, 536, 551] [69, 87, 117, 201, 243, 339, 369, 405, 447, 537, 551] [70, 88, 118, 202, 244, 340, 370, 406, 448, 538, 551] [71, 89, 119, 203, 245, 341, 371, 407, 449, 539, 551] [72, 90, 138, 168, 264, 336, 342, 426, 450, 486, 552] [73, 91, 139, 169, 265, 337, 343, 427, 451, 487, 552] [74, 92, 140, 170, 266, 338, 344, 428, 452, 488, 552] [75, 93, 141, 171, 267, 339, 345, 429, 453, 489, 552] [76, 94, 142, 172, 268, 340, 346, 430, 454, 490, 552] [77, 95, 143, 173, 269, 341, 347, 431, 455, 491, 552] [78, 96, 126, 174, 252, 324, 348, 414, 456, 492, 553] [79, 97, 127, 175, 253, 325, 349, 415, 457, 493, 553] [80, 98, 128, 176, 254, 326, 350, 416, 458, 494, 553] [81, 99, 129, 177, 255, 327, 351, 417, 459, 495, 553] [82, 100, 130, 178, 256, 328, 352, 418, 460, 496, 553] [83, 101, 131, 179, 257, 329, 353, 419, 461, 497, 553] [54, 90, 156, 186, 228, 354, 360, 390, 468, 504, 554] [55, 91, 157, 187, 229, 355, 361, 391, 469, 505, 554] [56, 92, 158, 188, 230, 356, 362, 392, 470, 506, 554] [57, 93, 159, 189, 231, 357, 363, 393, 471, 507, 554] [58, 94, 160, 190, 232, 358, 364, 394, 472, 508, 554] [59, 95, 161, 191, 233, 359, 365, 395, 473, 509, 554] [60, 96, 144, 192, 216, 342, 366, 378, 474, 510, 555] [61, 97, 145, 193, 217, 343, 367, 379, 475, 511, 555] [62, 98, 146, 194, 218, 344, 368, 380, 476, 512, 555] [63, 99, 147, 195, 219, 345, 369, 381, 477, 513, 555] [64, 100, 148, 196, 220, 346, 370, 382, 478, 514, 555] [65, 101, 149, 197, 221, 347, 371, 383, 479, 515, 555] [66, 102, 150, 180, 222, 348, 372, 384, 480, 516, 556] [67, 103, 151, 181, 223, 349, 373, 385, 481, 517, 556] [68, 104, 152, 182, 224, 350, 374, 386, 482, 518, 556] [69, 105, 153, 183, 225, 351, 375, 387, 483, 519, 556] [70, 106, 154, 184, 226, 352, 376, 388, 484, 520, 556] [71, 107, 155, 185, 227, 353, 377, 389, 485, 521, 556] [30, 108, 126, 174, 258, 306, 378, 426, 462, 486, 557] [31, 109, 127, 175, 259, 307, 379, 427, 463, 487, 557] [32, 110, 128, 176, 260, 308, 380, 428, 464, 488, 557] [33, 111, 129, 177, 261, 309, 381, 429, 465, 489, 557] [34, 112, 130, 178, 262, 310, 382, 430, 466, 490, 557] [35, 113, 131, 179, 263, 311, 383, 431, 467, 491, 557] [18, 114, 132, 162, 264, 312, 384, 414, 450, 492, 558] [19, 115, 133, 163, 265, 313, 385, 415, 451, 493, 558] [20, 116, 134, 164, 266, 314, 386, 416, 452, 494, 558] [21, 117, 135, 165, 267, 315, 387, 417, 453, 495, 558] [22, 118, 136, 166, 268, 316, 388, 418, 454, 496, 558] [23, 119, 137, 167, 269, 317, 389, 419, 455, 497, 558] [24, 120, 138, 168, 252, 318, 390, 420, 456, 498, 559] [25, 121, 139, 169, 253, 319, 391, 421, 457, 499, 559] [26, 122, 140, 170, 254, 320, 392, 422, 458, 500, 559] [27, 123, 141, 171, 255, 321, 393, 423, 459, 501, 559] [28, 124, 142, 172, 256, 322, 394, 424, 460, 502, 559] [29, 125, 143, 173, 257, 323, 395, 425, 461, 503, 559] [48, 126, 144, 192, 222, 270, 390, 396, 480, 504, 560] [49, 127, 145, 193, 223, 271, 391, 397, 481, 505, 560] [50, 128, 146, 194, 224, 272, 392, 398, 482, 506, 560] [51, 129, 147, 195, 225, 273, 393, 399, 483, 507, 560] [52, 130, 148, 196, 226, 274, 394, 400, 484, 508, 560] [53, 131, 149, 197, 227, 275, 395, 401, 485, 509, 560] [36, 132, 150, 180, 228, 276, 378, 402, 468, 510, 561] [37, 133, 151, 181, 229, 277, 379, 403, 469, 511, 561] [38, 134, 152, 182, 230, 278, 380, 404, 470, 512, 561] [39, 135, 153, 183, 231, 279, 381, 405, 471, 513, 561] [40, 136, 154, 184, 232, 280, 382, 406, 472, 514, 561] [41, 137, 155, 185, 233, 281, 383, 407, 473, 515, 561] [42, 138, 156, 186, 216, 282, 384, 408, 474, 516, 562] [43, 139, 157, 187, 217, 283, 385, 409, 475, 517, 562] [44, 140, 158, 188, 218, 284, 386, 410, 476, 518, 562] [45, 141, 159, 189, 219, 285, 387, 411, 477, 519, 562] [46, 142, 160, 190, 220, 286, 388, 412, 478, 520, 562] [47, 143, 161, 191, 221, 287, 389, 413, 479, 521, 562] [12, 108, 144, 210, 240, 288, 408, 414, 444, 522, 563] [13, 109, 145, 211, 241, 289, 409, 415, 445, 523, 563] [14, 110, 146, 212, 242, 290, 410, 416, 446, 524, 563] [15, 111, 147, 213, 243, 291, 411, 417, 447, 525, 563] [16, 112, 148, 214, 244, 292, 412, 418, 448, 526, 563] [17, 113, 149, 215, 245, 293, 413, 419, 449, 527, 563] [0, 114, 150, 198, 246, 294, 396, 420, 432, 528, 564] [1, 115, 151, 199, 247, 295, 397, 421, 433, 529, 564] [2, 116, 152, 200, 248, 296, 398, 422, 434, 530, 564] [3, 117, 153, 201, 249, 297, 399, 423, 435, 531, 564] [4, 118, 154, 202, 250, 298, 400, 424, 436, 532, 564] [5, 119, 155, 203, 251, 299, 401, 425, 437, 533, 564] [6, 120, 156, 204, 234, 300, 402, 426, 438, 534, 565] [7, 121, 157, 205, 235, 301, 403, 427, 439, 535, 565] [8, 122, 158, 206, 236, 302, 404, 428, 440, 536, 565] [9, 123, 159, 207, 237, 303, 405, 429, 441, 537, 565] [10, 124, 160, 208, 238, 304, 406, 430, 442, 538, 565] [11, 125, 161, 209, 239, 305, 407, 431, 443, 539, 565] [42, 84, 162, 180, 228, 270, 360, 432, 480, 516, 566] [43, 85, 163, 181, 229, 271, 361, 433, 481, 517, 566] [44, 86, 164, 182, 230, 272, 362, 434, 482, 518, 566] [45, 87, 165, 183, 231, 273, 363, 435, 483, 519, 566] [46, 88, 166, 184, 232, 274, 364, 436, 484, 520, 566] [47, 89, 167, 185, 233, 275, 365, 437, 485, 521, 566] [48, 72, 168, 186, 216, 276, 366, 438, 468, 504, 567] [49, 73, 169, 187, 217, 277, 367, 439, 469, 505, 567] [50, 74, 170, 188, 218, 278, 368, 440, 470, 506, 567] [51, 75, 171, 189, 219, 279, 369, 441, 471, 507, 567] [52, 76, 172, 190, 220, 280, 370, 442, 472, 508, 567] [53, 77, 173, 191, 221, 281, 371, 443, 473, 509, 567] [36, 78, 174, 192, 222, 282, 372, 444, 474, 510, 568] [37, 79, 175, 193, 223, 283, 373, 445, 475, 511, 568] [38, 80, 176, 194, 224, 284, 374, 446, 476, 512, 568] [39, 81, 177, 195, 225, 285, 375, 447, 477, 513, 568] [40, 82, 178, 196, 226, 286, 376, 448, 478, 514, 568] [41, 83, 179, 197, 227, 287, 377, 449, 479, 515, 568] [12, 90, 186, 204, 234, 294, 330, 432, 456, 522, 569] [13, 91, 187, 205, 235, 295, 331, 433, 457, 523, 569] [14, 92, 188, 206, 236, 296, 332, 434, 458, 524, 569] [15, 93, 189, 207, 237, 297, 333, 435, 459, 525, 569] [16, 94, 190, 208, 238, 298, 334, 436, 460, 526, 569] [17, 95, 191, 209, 239, 299, 335, 437, 461, 527, 569] [0, 96, 192, 210, 240, 300, 336, 438, 462, 528, 570] [1, 97, 193, 211, 241, 301, 337, 439, 463, 529, 570] [2, 98, 194, 212, 242, 302, 338, 440, 464, 530, 570] [3, 99, 195, 213, 243, 303, 339, 441, 465, 531, 570] [4, 100, 196, 214, 244, 304, 340, 442, 466, 532, 570] [5, 101, 197, 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Code ID 618-48-24 · download JSON · raw on GitHub