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[[648,18,23]] d ≤
n
648
k
18
d
23
kd²/n
14.694
w
8
X/Z
1.17
g
0.0454
r
4.2426
layers
2
swaps
2175

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Distance

X/Z asymmetry 1.17 · d_X ≤ 23, d_Z ≤ 27 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 23 · witness weight 23 (claimed upper_bound)
witness operator (support, 23 qubits)
[240, 259, 274, 295, 308, 310, 340, 353, 366, 391, 404, 420, 423, 426, 442, 461, 474, 496, 512, 528, 531, 566, 582]
d_Z 27 · witness weight 27 (claimed upper_bound)
witness operator (support, 27 qubits)
[153, 169, 174, 185, 190, 192, 204, 207, 211, 215, 216, 239, 242, 480, 516, 519, 528, 533, 537, 538, 541, 542, 543, 549, 558, 562, 568]
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 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 2–8 (mean 6.909) · H_Z 3–8 (mean 6.857)
qubit degrees H_X 1–6 (mean 3.519) · H_Z 1–4 (mean 3.333)
trapping sets H_X (1,1)×51 (2,1)×124 (3,0)×45 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 51 (1,2): 100 (1,3): 57 (1,4): 354 (1,5): 74 (1,6): 12 (2,1): 124 (2,2): 153 (2,3): 404 (2,4): 737 (2,5): 576 (2,6): 3938 (2,7): 644 (2,8): 299 (2,9): 134 (2,10): 11 (3,0): 45 (3,1): 149 (3,2): 474 (3,3): 1859 (3,4): 3095 (3,5): 6366 (3,6): 13910 (3,7): 11351 (3,8): 61073 (3,9): 11879 (3,10): 12014 (3,11): 3583 (3,12): 2024 (3,13): 455 (3,14): 46
trapping sets H_Z (1,1)×54 (2,0)×15 (3,0)×15 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 54 (1,2): 108 (1,3): 54 (1,4): 432 (2,0): 15 (2,1): 116 (2,2): 227 (2,3): 376 (2,4): 760 (2,5): 594 (2,6): 4797 (3,0): 15 (3,1): 205 (3,2): 678 (3,3): 1682 (3,4): 3546 (3,5): 6640 (3,6): 15124 (3,7): 11088 (3,8): 75933 (3,9): 969 (3,10): 8460
witness diameter X 22.0227 · Z 17.1172 (Euclidean support diameter of the stored distance witnesses in the layout; an upper bound on the exhibited logicals’ spread, not a minimum over all logicals)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 4.243
X checkZ checkqubit site (324)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release
routing cost 2175 nearest-neighbor SWAPs per round in total, at most 4 for one check (heuristic: MST lower bound on the layout, with one lattice step = the minimum qubit spacing 1; not a rank)

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction Open-boundary weight-8 planar bivariate-bicycle (tile) code from research/local2d/boundary_engine.build_planar(18x18,S_F_TILE4,S_G_TILE4_MAIN), the board's tile bulk (the B=4 tile of arXiv:2504.09171, two support swaps, same as codes/924-18-31.json), on a 18x18 lattice: n=2*18*18=648, k=18, max check weight 8, bilayer layout from research/local2d/planar.grid_coordinates (A(i,j) and B(i,j) share site (i,j), interaction radius 4.2426). Fills the n in (578,792) hole in the k=18 tile ladder, which jumped codes/578-18-20.json -> codes/792-18-27.json: those sizes were never built. Screened at 60000 and 400000 gf2_fast RIS trials, then re-measured at 1500000 fresh-seed fast trials.
model MiMo-V2.6-Flash (OpenCode agent harness) (claimed, not verified)
date 2026-10-16
family tile (a tag, not a ranking)
locality 2D-local bilayer (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

[[648,18,23]] — open-boundary tile code on an 18x18 lattice (weight-8, bilayer)

Direction & hypothesis

Cell weight-8 / local-2d-bilayer, family tile. Same opening as its siblings [[612,18,21]] and [[722,18,25]]: the k=18 tile ladder jumped from codes/578-18-20.json to codes/792-18-27.json with nothing in between, and the hypothesis was that those sizes were simply never built. The working prediction — that d is set by min(Lx, Ly) and therefore steps in even-ish jumps rather than smoothly in n — makes an 18x18 lattice the rung-23 size.

What was searched

Every lattice (Lx, Ly) with Lx <= Ly in [14, 23]^2 and 2 Lx Ly inside (578, 792) — 24 of them — built with `research/local2d/boundary_engine. build_planar(Lx, Ly, S_F_TILE4, S_G_TILE4_MAIN)`, after calibrating the generator against codes/924-18-31.json by X and Z check-matrix equality. Screening 60,000 gf2_fast RIS trials per lattice, survivors deepened to 400,000 fast trials, every packaged candidate put through the real gate (verify/validate_candidate.py, run unchanged via research/kit/coordination.py). Layout from research/local2d/planar.grid_coordinates, layers=2, interaction radius 4.2426.

Evidence trail

  • 60,000 fast trials: d <= 24
  • 400,000 fast trials (packaging): d <= 23, X witness of weight 23
  • 1,500,000 fast trials, fresh seed 101: d <= 23 still (X 23, Z 28

    • measured separately at the NumPy budget)

  • CI's gate re-verifies at PR time with a deeper fresh-seed pass

Witness-backed upper bound, not exact: k=18 is far outside the certifier's measured envelope (verify/certify.py has certified only d <= 13 and k <= 12 today), so d<= is the honest and only label available. The claim is refutation-tested at PR time and again by the weekly board sweep.

Dead ends

  • The 16x\* and 17x\* sizes around this one carry d <= 20 and d <= 21

    • respectively; the 17x\* codes advance the cell and are submitted as their own entries, the 16x\* ones are dominated by codes/578-18-20.json.

  • [[720,18,24]], an 18x20 lattice, collapsed from d <= 24 to d <= 23 at

    • the 1.5M-trial confirmation. It is the same rung as this entry at a larger n, so it was not promoted; rung 24 was left unfilled rather than claimed on a soft measurement.

  • [[722,18,26]] (19x19) collapsed from 26 to 25 at the same depth and was

    • re-staged at the deeper number before promotion.

  • No lattice witnessed d=22 at any budget.

Tools

Model: MiMo-V2.6-Flash, driven as an OpenCode agent harness. Repository tooling only: research/local2d/boundary_engine.py, research/local2d/planar.py, research/kit/surrogate.py with the gf2_fast accelerator (make fast), research/kit/submit.py, research/kit/coordination.py. About 15 CPU core-hours for the shared sweep, ~2M fast trials behind this entry's own claim.

Reproduction

import sys; sys.path[:0] = ["research/kit", "research/local2d", "verify"]
from boundary_engine import build_planar, S_F_TILE4, S_G_TILE4_MAIN
from planar import grid_coordinates
HX, HZ, info = build_planar(18, 18, S_F_TILE4, S_G_TILE4_MAIN)   # [[648,18,23]]
coords = grid_coordinates(18, 18, kept=info.get("kept_qubits"))

Same bulk supports as codes/924-18-31.json (S_F_TILE4, S_G_TILE4_MAIN); only the lattice size differs.

Parity checks

X-checks 330 (max weight 8) · Z-checks 315 (max weight 8)
H_X (330 checks, sparse supports)
[0, 3, 38, 54, 326, 345, 360, 381] [1, 4, 39, 55, 327, 346, 361, 382] [2, 5, 40, 56, 328, 347, 362, 383] [3, 6, 41, 57, 329, 348, 363, 384] [4, 7, 42, 58, 330, 349, 364, 385] [5, 8, 43, 59, 331, 350, 365, 386] [6, 9, 44, 60, 332, 351, 366, 387] [7, 10, 45, 61, 333, 352, 367, 388] [8, 11, 46, 62, 334, 353, 368, 389] [9, 12, 47, 63, 335, 354, 369, 390] [10, 13, 48, 64, 336, 355, 370, 391] [11, 14, 49, 65, 337, 356, 371, 392] [12, 15, 50, 66, 338, 357, 372, 393] [13, 16, 51, 67, 339, 358, 373, 394] [14, 17, 52, 68, 340, 359, 374, 395] [18, 21, 56, 72, 344, 363, 378, 399] [19, 22, 57, 73, 345, 364, 379, 400] [20, 23, 58, 74, 346, 365, 380, 401] [21, 24, 59, 75, 347, 366, 381, 402] [22, 25, 60, 76, 348, 367, 382, 403] [23, 26, 61, 77, 349, 368, 383, 404] [24, 27, 62, 78, 350, 369, 384, 405] [25, 28, 63, 79, 351, 370, 385, 406] [26, 29, 64, 80, 352, 371, 386, 407] [27, 30, 65, 81, 353, 372, 387, 408] [28, 31, 66, 82, 354, 373, 388, 409] [29, 32, 67, 83, 355, 374, 389, 410] [30, 33, 68, 84, 356, 375, 390, 411] [31, 34, 69, 85, 357, 376, 391, 412] [32, 35, 70, 86, 358, 377, 392, 413] [36, 39, 74, 90, 362, 381, 396, 417] [37, 40, 75, 91, 363, 382, 397, 418] [38, 41, 76, 92, 364, 383, 398, 419] [39, 42, 77, 93, 365, 384, 399, 420] [40, 43, 78, 94, 366, 385, 400, 421] [41, 44, 79, 95, 367, 386, 401, 422] [42, 45, 80, 96, 368, 387, 402, 423] [43, 46, 81, 97, 369, 388, 403, 424] [44, 47, 82, 98, 370, 389, 404, 425] [45, 48, 83, 99, 371, 390, 405, 426] [46, 49, 84, 100, 372, 391, 406, 427] [47, 50, 85, 101, 373, 392, 407, 428] [48, 51, 86, 102, 374, 393, 408, 429] [49, 52, 87, 103, 375, 394, 409, 430] [50, 53, 88, 104, 376, 395, 410, 431] [54, 57, 92, 108, 380, 399, 414, 435] [55, 58, 93, 109, 381, 400, 415, 436] [56, 59, 94, 110, 382, 401, 416, 437] [57, 60, 95, 111, 383, 402, 417, 438] [58, 61, 96, 112, 384, 403, 418, 439] [59, 62, 97, 113, 385, 404, 419, 440] [60, 63, 98, 114, 386, 405, 420, 441] [61, 64, 99, 115, 387, 406, 421, 442] [62, 65, 100, 116, 388, 407, 422, 443] [63, 66, 101, 117, 389, 408, 423, 444] [64, 67, 102, 118, 390, 409, 424, 445] [65, 68, 103, 119, 391, 410, 425, 446] [66, 69, 104, 120, 392, 411, 426, 447] [67, 70, 105, 121, 393, 412, 427, 448] [68, 71, 106, 122, 394, 413, 428, 449] [72, 75, 110, 126, 398, 417, 432, 453] [73, 76, 111, 127, 399, 418, 433, 454] [74, 77, 112, 128, 400, 419, 434, 455] [75, 78, 113, 129, 401, 420, 435, 456] [76, 79, 114, 130, 402, 421, 436, 457] [77, 80, 115, 131, 403, 422, 437, 458] [78, 81, 116, 132, 404, 423, 438, 459] [79, 82, 117, 133, 405, 424, 439, 460] [80, 83, 118, 134, 406, 425, 440, 461] [81, 84, 119, 135, 407, 426, 441, 462] [82, 85, 120, 136, 408, 427, 442, 463] [83, 86, 121, 137, 409, 428, 443, 464] [84, 87, 122, 138, 410, 429, 444, 465] [85, 88, 123, 139, 411, 430, 445, 466] [86, 89, 124, 140, 412, 431, 446, 467] [90, 93, 128, 144, 416, 435, 450, 471] [91, 94, 129, 145, 417, 436, 451, 472] [92, 95, 130, 146, 418, 437, 452, 473] [93, 96, 131, 147, 419, 438, 453, 474] [94, 97, 132, 148, 420, 439, 454, 475] [95, 98, 133, 149, 421, 440, 455, 476] [96, 99, 134, 150, 422, 441, 456, 477] [97, 100, 135, 151, 423, 442, 457, 478] [98, 101, 136, 152, 424, 443, 458, 479] [99, 102, 137, 153, 425, 444, 459, 480] [100, 103, 138, 154, 426, 445, 460, 481] [101, 104, 139, 155, 427, 446, 461, 482] [102, 105, 140, 156, 428, 447, 462, 483] [103, 106, 141, 157, 429, 448, 463, 484] [104, 107, 142, 158, 430, 449, 464, 485] [108, 111, 146, 162, 434, 453, 468, 489] [109, 112, 147, 163, 435, 454, 469, 490] [110, 113, 148, 164, 436, 455, 470, 491] [111, 114, 149, 165, 437, 456, 471, 492] [112, 115, 150, 166, 438, 457, 472, 493] [113, 116, 151, 167, 439, 458, 473, 494] [114, 117, 152, 168, 440, 459, 474, 495] [115, 118, 153, 169, 441, 460, 475, 496] [116, 119, 154, 170, 442, 461, 476, 497] [117, 120, 155, 171, 443, 462, 477, 498] [118, 121, 156, 172, 444, 463, 478, 499] [119, 122, 157, 173, 445, 464, 479, 500] [120, 123, 158, 174, 446, 465, 480, 501] [121, 124, 159, 175, 447, 466, 481, 502] [122, 125, 160, 176, 448, 467, 482, 503] [126, 129, 164, 180, 452, 471, 486, 507] [127, 130, 165, 181, 453, 472, 487, 508] [128, 131, 166, 182, 454, 473, 488, 509] [129, 132, 167, 183, 455, 474, 489, 510] [130, 133, 168, 184, 456, 475, 490, 511] [131, 134, 169, 185, 457, 476, 491, 512] [132, 135, 170, 186, 458, 477, 492, 513] [133, 136, 171, 187, 459, 478, 493, 514] [134, 137, 172, 188, 460, 479, 494, 515] [135, 138, 173, 189, 461, 480, 495, 516] [136, 139, 174, 190, 462, 481, 496, 517] [137, 140, 175, 191, 463, 482, 497, 518] [138, 141, 176, 192, 464, 483, 498, 519] [139, 142, 177, 193, 465, 484, 499, 520] [140, 143, 178, 194, 466, 485, 500, 521] [144, 147, 182, 198, 470, 489, 504, 525] [145, 148, 183, 199, 471, 490, 505, 526] [146, 149, 184, 200, 472, 491, 506, 527] [147, 150, 185, 201, 473, 492, 507, 528] [148, 151, 186, 202, 474, 493, 508, 529] [149, 152, 187, 203, 475, 494, 509, 530] [150, 153, 188, 204, 476, 495, 510, 531] [151, 154, 189, 205, 477, 496, 511, 532] [152, 155, 190, 206, 478, 497, 512, 533] [153, 156, 191, 207, 479, 498, 513, 534] [154, 157, 192, 208, 480, 499, 514, 535] [155, 158, 193, 209, 481, 500, 515, 536] [156, 159, 194, 210, 482, 501, 516, 537] [157, 160, 195, 211, 483, 502, 517, 538] [158, 161, 196, 212, 484, 503, 518, 539] [162, 165, 200, 216, 488, 507, 522, 543] [163, 166, 201, 217, 489, 508, 523, 544] [164, 167, 202, 218, 490, 509, 524, 545] [165, 168, 203, 219, 491, 510, 525, 546] [166, 169, 204, 220, 492, 511, 526, 547] [167, 170, 205, 221, 493, 512, 527, 548] [168, 171, 206, 222, 494, 513, 528, 549] [169, 172, 207, 223, 495, 514, 529, 550] [170, 173, 208, 224, 496, 515, 530, 551] [171, 174, 209, 225, 497, 516, 531, 552] [172, 175, 210, 226, 498, 517, 532, 553] [173, 176, 211, 227, 499, 518, 533, 554] [174, 177, 212, 228, 500, 519, 534, 555] [175, 178, 213, 229, 501, 520, 535, 556] [176, 179, 214, 230, 502, 521, 536, 557] [180, 183, 218, 234, 506, 525, 540, 561] [181, 184, 219, 235, 507, 526, 541, 562] [182, 185, 220, 236, 508, 527, 542, 563] [183, 186, 221, 237, 509, 528, 543, 564] [184, 187, 222, 238, 510, 529, 544, 565] [185, 188, 223, 239, 511, 530, 545, 566] [186, 189, 224, 240, 512, 531, 546, 567] [187, 190, 225, 241, 513, 532, 547, 568] [188, 191, 226, 242, 514, 533, 548, 569] [189, 192, 227, 243, 515, 534, 549, 570] [190, 193, 228, 244, 516, 535, 550, 571] [191, 194, 229, 245, 517, 536, 551, 572] [192, 195, 230, 246, 518, 537, 552, 573] [193, 196, 231, 247, 519, 538, 553, 574] [194, 197, 232, 248, 520, 539, 554, 575] [198, 201, 236, 252, 524, 543, 558, 579] [199, 202, 237, 253, 525, 544, 559, 580] [200, 203, 238, 254, 526, 545, 560, 581] [201, 204, 239, 255, 527, 546, 561, 582] [202, 205, 240, 256, 528, 547, 562, 583] [203, 206, 241, 257, 529, 548, 563, 584] [204, 207, 242, 258, 530, 549, 564, 585] [205, 208, 243, 259, 531, 550, 565, 586] [206, 209, 244, 260, 532, 551, 566, 587] [207, 210, 245, 261, 533, 552, 567, 588] [208, 211, 246, 262, 534, 553, 568, 589] [209, 212, 247, 263, 535, 554, 569, 590] [210, 213, 248, 264, 536, 555, 570, 591] [211, 214, 249, 265, 537, 556, 571, 592] [212, 215, 250, 266, 538, 557, 572, 593] [216, 219, 254, 270, 542, 561, 576, 597] [217, 220, 255, 271, 543, 562, 577, 598] [218, 221, 256, 272, 544, 563, 578, 599] [219, 222, 257, 273, 545, 564, 579, 600] [220, 223, 258, 274, 546, 565, 580, 601] [221, 224, 259, 275, 547, 566, 581, 602] [222, 225, 260, 276, 548, 567, 582, 603] [223, 226, 261, 277, 549, 568, 583, 604] [224, 227, 262, 278, 550, 569, 584, 605] [225, 228, 263, 279, 551, 570, 585, 606] [226, 229, 264, 280, 552, 571, 586, 607] [227, 230, 265, 281, 553, 572, 587, 608] [228, 231, 266, 282, 554, 573, 588, 609] [229, 232, 267, 283, 555, 574, 589, 610] [230, 233, 268, 284, 556, 575, 590, 611] [234, 237, 272, 288, 560, 579, 594, 615] [235, 238, 273, 289, 561, 580, 595, 616] [236, 239, 274, 290, 562, 581, 596, 617] [237, 240, 275, 291, 563, 582, 597, 618] [238, 241, 276, 292, 564, 583, 598, 619] [239, 242, 277, 293, 565, 584, 599, 620] [240, 243, 278, 294, 566, 585, 600, 621] [241, 244, 279, 295, 567, 586, 601, 622] [242, 245, 280, 296, 568, 587, 602, 623] [243, 246, 281, 297, 569, 588, 603, 624] [244, 247, 282, 298, 570, 589, 604, 625] [245, 248, 283, 299, 571, 590, 605, 626] [246, 249, 284, 300, 572, 591, 606, 627] [247, 250, 285, 301, 573, 592, 607, 628] [248, 251, 286, 302, 574, 593, 608, 629] [252, 255, 290, 306, 578, 597, 612, 633] [253, 256, 291, 307, 579, 598, 613, 634] [254, 257, 292, 308, 580, 599, 614, 635] [255, 258, 293, 309, 581, 600, 615, 636] [256, 259, 294, 310, 582, 601, 616, 637] [257, 260, 295, 311, 583, 602, 617, 638] [258, 261, 296, 312, 584, 603, 618, 639] [259, 262, 297, 313, 585, 604, 619, 640] [260, 263, 298, 314, 586, 605, 620, 641] [261, 264, 299, 315, 587, 606, 621, 642] [262, 265, 300, 316, 588, 607, 622, 643] [263, 266, 301, 317, 589, 608, 623, 644] [264, 267, 302, 318, 590, 609, 624, 645] [265, 268, 303, 319, 591, 610, 625, 646] [266, 269, 304, 320, 592, 611, 626, 647] [0, 327] [1, 328] [2, 329] [3, 330] [4, 331] [5, 332] [6, 333] [7, 334] [8, 335] [9, 336] [10, 337] [11, 338] [12, 339] [13, 340] [14, 341] [2, 18, 324, 345] [3, 19, 325, 346] [4, 20, 326, 347] [5, 21, 327, 348] [6, 22, 328, 349] [7, 23, 329, 350] [8, 24, 330, 351] [9, 25, 331, 352] [10, 26, 332, 353] [11, 27, 333, 354] [12, 28, 334, 355] [13, 29, 335, 356] [14, 30, 336, 357] [15, 31, 337, 358] [16, 32, 338, 359] [3, 38, 54, 326, 327, 345, 360, 381] [4, 39, 55, 327, 328, 346, 361, 382] [5, 40, 56, 328, 329, 347, 362, 383] [6, 41, 57, 329, 330, 348, 363, 384] [7, 42, 58, 330, 331, 349, 364, 385] [8, 43, 59, 331, 332, 350, 365, 386] [9, 44, 60, 332, 333, 351, 366, 387] [10, 45, 61, 333, 334, 352, 367, 388] [11, 46, 62, 334, 335, 353, 368, 389] [12, 47, 63, 335, 336, 354, 369, 390] [13, 48, 64, 336, 337, 355, 370, 391] [14, 49, 65, 337, 338, 356, 371, 392] [15, 50, 66, 338, 339, 357, 372, 393] [16, 51, 67, 339, 340, 358, 373, 394] [17, 52, 68, 340, 341, 359, 374, 395] [20, 36, 327, 342, 363] [21, 37, 328, 343, 364] [22, 38, 329, 344, 365] [23, 39, 330, 345, 366] [24, 40, 331, 346, 367] [25, 41, 332, 347, 368] [26, 42, 333, 348, 369] [27, 43, 334, 349, 370] [28, 44, 335, 350, 371] [29, 45, 336, 351, 372] [30, 46, 337, 352, 373] [31, 47, 338, 353, 374] [32, 48, 339, 354, 375] [33, 49, 340, 355, 376] [34, 50, 341, 356, 377] [270, 273, 308, 596, 615, 630] [271, 274, 309, 597, 616, 631] [272, 275, 310, 598, 617, 632] [273, 276, 311, 599, 618, 633] [274, 277, 312, 600, 619, 634] [275, 278, 313, 601, 620, 635] [276, 279, 314, 602, 621, 636] [277, 280, 315, 603, 622, 637] [278, 281, 316, 604, 623, 638] [279, 282, 317, 605, 624, 639] [280, 283, 318, 606, 625, 640] [281, 284, 319, 607, 626, 641] [282, 285, 320, 608, 627, 642] [283, 286, 321, 609, 628, 643] [284, 287, 322, 610, 629, 644] [288, 291, 614, 633] [289, 292, 615, 634] [290, 293, 616, 635] [291, 294, 617, 636] [292, 295, 618, 637] [293, 296, 619, 638] [294, 297, 620, 639] [295, 298, 621, 640] [296, 299, 622, 641] [297, 300, 623, 642] [298, 301, 624, 643] [299, 302, 625, 644] [300, 303, 626, 645] [301, 304, 627, 646] [302, 305, 628, 647] [306, 309, 632] [307, 310, 633] [308, 311, 634] [309, 312, 635] [310, 313, 636] [311, 314, 637] [312, 315, 638] [313, 316, 639] [314, 317, 640] [315, 318, 641] [316, 319, 642] [317, 320, 643] [318, 321, 644] [319, 322, 645] [320, 323, 646]
H_Z (315 checks, sparse supports)
[0, 21, 36, 55, 327, 343, 378, 381] [1, 22, 37, 56, 328, 344, 379, 382] [2, 23, 38, 57, 329, 345, 380, 383] [3, 24, 39, 58, 330, 346, 381, 384] [4, 25, 40, 59, 331, 347, 382, 385] [5, 26, 41, 60, 332, 348, 383, 386] [6, 27, 42, 61, 333, 349, 384, 387] [7, 28, 43, 62, 334, 350, 385, 388] [8, 29, 44, 63, 335, 351, 386, 389] [9, 30, 45, 64, 336, 352, 387, 390] [10, 31, 46, 65, 337, 353, 388, 391] [11, 32, 47, 66, 338, 354, 389, 392] [12, 33, 48, 67, 339, 355, 390, 393] [13, 34, 49, 68, 340, 356, 391, 394] [14, 35, 50, 69, 341, 357, 392, 395] [18, 39, 54, 73, 345, 361, 396, 399] [19, 40, 55, 74, 346, 362, 397, 400] [20, 41, 56, 75, 347, 363, 398, 401] [21, 42, 57, 76, 348, 364, 399, 402] [22, 43, 58, 77, 349, 365, 400, 403] [23, 44, 59, 78, 350, 366, 401, 404] [24, 45, 60, 79, 351, 367, 402, 405] [25, 46, 61, 80, 352, 368, 403, 406] [26, 47, 62, 81, 353, 369, 404, 407] [27, 48, 63, 82, 354, 370, 405, 408] [28, 49, 64, 83, 355, 371, 406, 409] [29, 50, 65, 84, 356, 372, 407, 410] [30, 51, 66, 85, 357, 373, 408, 411] [31, 52, 67, 86, 358, 374, 409, 412] [32, 53, 68, 87, 359, 375, 410, 413] [36, 57, 72, 91, 363, 379, 414, 417] [37, 58, 73, 92, 364, 380, 415, 418] [38, 59, 74, 93, 365, 381, 416, 419] [39, 60, 75, 94, 366, 382, 417, 420] [40, 61, 76, 95, 367, 383, 418, 421] [41, 62, 77, 96, 368, 384, 419, 422] [42, 63, 78, 97, 369, 385, 420, 423] [43, 64, 79, 98, 370, 386, 421, 424] [44, 65, 80, 99, 371, 387, 422, 425] [45, 66, 81, 100, 372, 388, 423, 426] [46, 67, 82, 101, 373, 389, 424, 427] [47, 68, 83, 102, 374, 390, 425, 428] [48, 69, 84, 103, 375, 391, 426, 429] [49, 70, 85, 104, 376, 392, 427, 430] [50, 71, 86, 105, 377, 393, 428, 431] [54, 75, 90, 109, 381, 397, 432, 435] [55, 76, 91, 110, 382, 398, 433, 436] [56, 77, 92, 111, 383, 399, 434, 437] [57, 78, 93, 112, 384, 400, 435, 438] [58, 79, 94, 113, 385, 401, 436, 439] [59, 80, 95, 114, 386, 402, 437, 440] [60, 81, 96, 115, 387, 403, 438, 441] [61, 82, 97, 116, 388, 404, 439, 442] [62, 83, 98, 117, 389, 405, 440, 443] [63, 84, 99, 118, 390, 406, 441, 444] [64, 85, 100, 119, 391, 407, 442, 445] [65, 86, 101, 120, 392, 408, 443, 446] [66, 87, 102, 121, 393, 409, 444, 447] [67, 88, 103, 122, 394, 410, 445, 448] [68, 89, 104, 123, 395, 411, 446, 449] [72, 93, 108, 127, 399, 415, 450, 453] [73, 94, 109, 128, 400, 416, 451, 454] [74, 95, 110, 129, 401, 417, 452, 455] [75, 96, 111, 130, 402, 418, 453, 456] [76, 97, 112, 131, 403, 419, 454, 457] [77, 98, 113, 132, 404, 420, 455, 458] [78, 99, 114, 133, 405, 421, 456, 459] [79, 100, 115, 134, 406, 422, 457, 460] [80, 101, 116, 135, 407, 423, 458, 461] [81, 102, 117, 136, 408, 424, 459, 462] [82, 103, 118, 137, 409, 425, 460, 463] [83, 104, 119, 138, 410, 426, 461, 464] [84, 105, 120, 139, 411, 427, 462, 465] [85, 106, 121, 140, 412, 428, 463, 466] [86, 107, 122, 141, 413, 429, 464, 467] [90, 111, 126, 145, 417, 433, 468, 471] [91, 112, 127, 146, 418, 434, 469, 472] [92, 113, 128, 147, 419, 435, 470, 473] [93, 114, 129, 148, 420, 436, 471, 474] [94, 115, 130, 149, 421, 437, 472, 475] [95, 116, 131, 150, 422, 438, 473, 476] [96, 117, 132, 151, 423, 439, 474, 477] [97, 118, 133, 152, 424, 440, 475, 478] [98, 119, 134, 153, 425, 441, 476, 479] [99, 120, 135, 154, 426, 442, 477, 480] [100, 121, 136, 155, 427, 443, 478, 481] [101, 122, 137, 156, 428, 444, 479, 482] [102, 123, 138, 157, 429, 445, 480, 483] [103, 124, 139, 158, 430, 446, 481, 484] [104, 125, 140, 159, 431, 447, 482, 485] [108, 129, 144, 163, 435, 451, 486, 489] [109, 130, 145, 164, 436, 452, 487, 490] [110, 131, 146, 165, 437, 453, 488, 491] [111, 132, 147, 166, 438, 454, 489, 492] [112, 133, 148, 167, 439, 455, 490, 493] [113, 134, 149, 168, 440, 456, 491, 494] [114, 135, 150, 169, 441, 457, 492, 495] [115, 136, 151, 170, 442, 458, 493, 496] [116, 137, 152, 171, 443, 459, 494, 497] [117, 138, 153, 172, 444, 460, 495, 498] [118, 139, 154, 173, 445, 461, 496, 499] [119, 140, 155, 174, 446, 462, 497, 500] [120, 141, 156, 175, 447, 463, 498, 501] [121, 142, 157, 176, 448, 464, 499, 502] [122, 143, 158, 177, 449, 465, 500, 503] [126, 147, 162, 181, 453, 469, 504, 507] [127, 148, 163, 182, 454, 470, 505, 508] [128, 149, 164, 183, 455, 471, 506, 509] [129, 150, 165, 184, 456, 472, 507, 510] [130, 151, 166, 185, 457, 473, 508, 511] [131, 152, 167, 186, 458, 474, 509, 512] [132, 153, 168, 187, 459, 475, 510, 513] [133, 154, 169, 188, 460, 476, 511, 514] [134, 155, 170, 189, 461, 477, 512, 515] [135, 156, 171, 190, 462, 478, 513, 516] [136, 157, 172, 191, 463, 479, 514, 517] [137, 158, 173, 192, 464, 480, 515, 518] [138, 159, 174, 193, 465, 481, 516, 519] [139, 160, 175, 194, 466, 482, 517, 520] [140, 161, 176, 195, 467, 483, 518, 521] [144, 165, 180, 199, 471, 487, 522, 525] [145, 166, 181, 200, 472, 488, 523, 526] [146, 167, 182, 201, 473, 489, 524, 527] [147, 168, 183, 202, 474, 490, 525, 528] [148, 169, 184, 203, 475, 491, 526, 529] [149, 170, 185, 204, 476, 492, 527, 530] [150, 171, 186, 205, 477, 493, 528, 531] [151, 172, 187, 206, 478, 494, 529, 532] [152, 173, 188, 207, 479, 495, 530, 533] [153, 174, 189, 208, 480, 496, 531, 534] [154, 175, 190, 209, 481, 497, 532, 535] [155, 176, 191, 210, 482, 498, 533, 536] [156, 177, 192, 211, 483, 499, 534, 537] [157, 178, 193, 212, 484, 500, 535, 538] [158, 179, 194, 213, 485, 501, 536, 539] [162, 183, 198, 217, 489, 505, 540, 543] [163, 184, 199, 218, 490, 506, 541, 544] [164, 185, 200, 219, 491, 507, 542, 545] [165, 186, 201, 220, 492, 508, 543, 546] [166, 187, 202, 221, 493, 509, 544, 547] [167, 188, 203, 222, 494, 510, 545, 548] [168, 189, 204, 223, 495, 511, 546, 549] [169, 190, 205, 224, 496, 512, 547, 550] [170, 191, 206, 225, 497, 513, 548, 551] [171, 192, 207, 226, 498, 514, 549, 552] [172, 193, 208, 227, 499, 515, 550, 553] [173, 194, 209, 228, 500, 516, 551, 554] [174, 195, 210, 229, 501, 517, 552, 555] [175, 196, 211, 230, 502, 518, 553, 556] [176, 197, 212, 231, 503, 519, 554, 557] [180, 201, 216, 235, 507, 523, 558, 561] [181, 202, 217, 236, 508, 524, 559, 562] [182, 203, 218, 237, 509, 525, 560, 563] [183, 204, 219, 238, 510, 526, 561, 564] [184, 205, 220, 239, 511, 527, 562, 565] [185, 206, 221, 240, 512, 528, 563, 566] [186, 207, 222, 241, 513, 529, 564, 567] [187, 208, 223, 242, 514, 530, 565, 568] [188, 209, 224, 243, 515, 531, 566, 569] [189, 210, 225, 244, 516, 532, 567, 570] [190, 211, 226, 245, 517, 533, 568, 571] [191, 212, 227, 246, 518, 534, 569, 572] [192, 213, 228, 247, 519, 535, 570, 573] [193, 214, 229, 248, 520, 536, 571, 574] [194, 215, 230, 249, 521, 537, 572, 575] [198, 219, 234, 253, 525, 541, 576, 579] [199, 220, 235, 254, 526, 542, 577, 580] [200, 221, 236, 255, 527, 543, 578, 581] [201, 222, 237, 256, 528, 544, 579, 582] [202, 223, 238, 257, 529, 545, 580, 583] [203, 224, 239, 258, 530, 546, 581, 584] [204, 225, 240, 259, 531, 547, 582, 585] [205, 226, 241, 260, 532, 548, 583, 586] [206, 227, 242, 261, 533, 549, 584, 587] [207, 228, 243, 262, 534, 550, 585, 588] [208, 229, 244, 263, 535, 551, 586, 589] [209, 230, 245, 264, 536, 552, 587, 590] [210, 231, 246, 265, 537, 553, 588, 591] [211, 232, 247, 266, 538, 554, 589, 592] [212, 233, 248, 267, 539, 555, 590, 593] [216, 237, 252, 271, 543, 559, 594, 597] [217, 238, 253, 272, 544, 560, 595, 598] [218, 239, 254, 273, 545, 561, 596, 599] [219, 240, 255, 274, 546, 562, 597, 600] [220, 241, 256, 275, 547, 563, 598, 601] [221, 242, 257, 276, 548, 564, 599, 602] [222, 243, 258, 277, 549, 565, 600, 603] [223, 244, 259, 278, 550, 566, 601, 604] [224, 245, 260, 279, 551, 567, 602, 605] [225, 246, 261, 280, 552, 568, 603, 606] [226, 247, 262, 281, 553, 569, 604, 607] [227, 248, 263, 282, 554, 570, 605, 608] [228, 249, 264, 283, 555, 571, 606, 609] [229, 250, 265, 284, 556, 572, 607, 610] [230, 251, 266, 285, 557, 573, 608, 611] [234, 255, 270, 289, 561, 577, 612, 615] [235, 256, 271, 290, 562, 578, 613, 616] [236, 257, 272, 291, 563, 579, 614, 617] [237, 258, 273, 292, 564, 580, 615, 618] [238, 259, 274, 293, 565, 581, 616, 619] [239, 260, 275, 294, 566, 582, 617, 620] [240, 261, 276, 295, 567, 583, 618, 621] [241, 262, 277, 296, 568, 584, 619, 622] [242, 263, 278, 297, 569, 585, 620, 623] [243, 264, 279, 298, 570, 586, 621, 624] [244, 265, 280, 299, 571, 587, 622, 625] [245, 266, 281, 300, 572, 588, 623, 626] [246, 267, 282, 301, 573, 589, 624, 627] [247, 268, 283, 302, 574, 590, 625, 628] [248, 269, 284, 303, 575, 591, 626, 629] [252, 273, 288, 307, 579, 595, 630, 633] [253, 274, 289, 308, 580, 596, 631, 634] [254, 275, 290, 309, 581, 597, 632, 635] [255, 276, 291, 310, 582, 598, 633, 636] [256, 277, 292, 311, 583, 599, 634, 637] [257, 278, 293, 312, 584, 600, 635, 638] [258, 279, 294, 313, 585, 601, 636, 639] [259, 280, 295, 314, 586, 602, 637, 640] [260, 281, 296, 315, 587, 603, 638, 641] [261, 282, 297, 316, 588, 604, 639, 642] [262, 283, 298, 317, 589, 605, 640, 643] [263, 284, 299, 318, 590, 606, 641, 644] [264, 285, 300, 319, 591, 607, 642, 645] [265, 286, 301, 320, 592, 608, 643, 646] [266, 287, 302, 321, 593, 609, 644, 647] [18, 324, 378] [36, 342, 396] [54, 360, 414] [72, 378, 432] [90, 396, 450] [108, 414, 468] [126, 432, 486] [144, 450, 504] [162, 468, 522] [180, 486, 540] [198, 504, 558] [216, 522, 576] [234, 540, 594] [252, 558, 612] [270, 576, 630] [19, 325, 379] [37, 343, 397] [55, 361, 415] [73, 379, 433] [91, 397, 451] [109, 415, 469] [127, 433, 487] [145, 451, 505] [163, 469, 523] [181, 487, 541] [199, 505, 559] [217, 523, 577] [235, 541, 595] [253, 559, 613] [271, 577, 631] [20, 54, 326, 342, 380] [38, 72, 344, 360, 398] [56, 90, 362, 378, 416] [74, 108, 380, 396, 434] [92, 126, 398, 414, 452] [110, 144, 416, 432, 470] [128, 162, 434, 450, 488] [146, 180, 452, 468, 506] [164, 198, 470, 486, 524] [182, 216, 488, 504, 542] [200, 234, 506, 522, 560] [218, 252, 524, 540, 578] [236, 270, 542, 558, 596] [254, 288, 560, 576, 614] [272, 306, 578, 594, 632] [16, 52, 71, 359, 394] [34, 70, 89, 377, 412] [52, 88, 107, 395, 430] [70, 106, 125, 413, 448] [88, 124, 143, 431, 466] [106, 142, 161, 449, 484] [124, 160, 179, 467, 502] [142, 178, 197, 485, 520] [160, 196, 215, 503, 538] [178, 214, 233, 521, 556] [196, 232, 251, 539, 574] [214, 250, 269, 557, 592] [232, 268, 287, 575, 610] [250, 286, 305, 593, 628] [268, 304, 323, 611, 646] [15, 51, 70, 358, 393] [33, 69, 88, 376, 411] [51, 87, 106, 394, 429] [69, 105, 124, 412, 447] [87, 123, 142, 430, 465] [105, 141, 160, 448, 483] [123, 159, 178, 466, 501] [141, 177, 196, 484, 519] [159, 195, 214, 502, 537] [177, 213, 232, 520, 555] [195, 231, 250, 538, 573] [213, 249, 268, 556, 591] [231, 267, 286, 574, 609] [249, 285, 304, 592, 627] [267, 303, 322, 610, 645] [17, 53, 395] [35, 71, 413] [53, 89, 431] [71, 107, 449] [89, 125, 467] [107, 143, 485] [125, 161, 503] [143, 179, 521] [161, 197, 539] [179, 215, 557] [197, 233, 575] [215, 251, 593] [233, 269, 611] [251, 287, 629] [269, 305, 647]
Code ID 648-18-23 · download JSON · raw on GitHub