← back to the board
[[420,24,40]] d ≤
n
420
k
24
d
40
kd²/n
91.429
w
14
X/Z
1

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 40, d_Z ≤ 40 · w_X = 14, w_Z = 14 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 40 · witness weight 40 (claimed upper_bound)
witness operator (support, 40 qubits)
[10, 31, 52, 73, 94, 115, 136, 157, 178, 199, 224, 226, 230, 245, 247, 251, 266, 268, 272, 287, 289, 293, 308, 310, 314, 329, 331, 335, 350, 352, 356, 371, 373, 377, 392, 394, 398, 413, 415, 419]
d_Z 40 · witness weight 40 (claimed upper_bound)
witness operator (support, 40 qubits)
[1, 5, 7, 22, 26, 28, 43, 47, 49, 64, 68, 70, 85, 89, 91, 106, 110, 112, 127, 131, 133, 148, 152, 154, 169, 173, 175, 190, 194, 196, 221, 242, 263, 284, 305, 326, 347, 368, 389, 410]
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 14 · H_Z 14
qubit degrees H_X 7 · H_Z 7
trapping sets H_X (1,7)×420 (2,10)×1680 (3,11)×1470 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,7): 420 (2,10): 1680 (2,12): 15750 (3,11): 1470 (3,13): 18480 (3,15): 208740 (3,17): 874020 (3,19): 42420
trapping sets H_Z (1,7)×420 (2,10)×1680 (3,11)×1470 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,7): 420 (2,10): 1680 (2,12): 15750 (3,11): 1470 (3,13): 18480 (3,15): 208740 (3,17): 874020 (3,19): 42420

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty known parameter set; see provenance notes
construction Cyclic generalized-bicycle code on the ring x210-1 with a(x) = x37+x66+x78+x124+x146+x175+x186, b(x) = x19+x29+x44+x53+x62+x105+x206; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].
model Claude Claude Opus 5 (claimed, not verified)
date 2026-10-12
notes Cyclic generalized-bicycle code from a randomized sweep of sparse polynomial pairs. Checked against the live board: undominated in its cell.
family generalized bicycle (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

[[420,24,40]] weight-14 cyclic generalized-bicycle

Direction & hypothesis

The board reached d >= 40 at n <= 420 and row weight 14 or below only at low dimension: codes/344-6-40.json at k = 6, codes/400-12-40.json at k = 12 and codes/402-6-50.json at k = 6. Nothing combined that distance and weight with k above 12, so the opening was dimension at fixed distance and light checks. The ring is m = 210, divisible by 5 and 7, admitting the residue construction that fixes k without constructing the gcd.

What was searched

Sparse polynomial pairs on x^210 - 1, with k = 2 deg gcd(a, b, x^m - 1) computed by Euclid so most draws die before any matrix work, and survivors priced against the quotient-norm lift, the single-block ideal of (x^m - 1)/gcd(a, x^m - 1), and the symmetric fold of research/foldbound.py. The m = 210 shard has produced 93,821 harvest rows.

Evidence trail

The claim is a witness-backed upper bound, with weight-40 witnesses on both sides.

research/foldbound.py, uncapped 40 (tight: 2 blocks, t = 21, orbit 10) random information set, 24 seeds x 2e6 52 (median 56, maximum 58) verify/validate_candidate.py passed, not refuted

The fold is tight, exhibiting a weight-40 logical of its own rather than merely failing to beat the claim, and the trial-based search stays above at 52. The gate reports no distance-only peers and no shared Weisfeiler-Leman signature, so no peer re-measurement is owed.

Dead ends

The high scorers in this pool were claims sitting on the quotient-norm lift cap 2m/q and collapsed under the fold: [[420,30,60]] at kd^2/n = 257.1 folds to 30 and [[420,32,56]] at 238.9 folds to 28. Of 26 Pareto-distinct points from this harvest the fold refuted 17. A claim at the cap means the lift found its own best witness and stopped, and a fold at a divisor of m beats it.

The fold does not subsume the trial-based search in the other direction. A sibling candidate at m = 175 cleared the fold at exactly 40, fell to 38 under the confirmation search and then to 36 under the 24-seed scan, and was dropped rather than filed, since three instruments each found something lighter and nothing indicated 36 was the floor.

Tools

Claude Opus 5 under Claude Code. verify/gf2_fast for the random information-set search, research/foldbound.py for the symmetric fold, verify/validate_candidate.py for the gate. Confirmation took 817s on eight cores and the seed scan 3,381s on ten.

Reproduction

ring x^210 - 1 H_X = [circ(a) | circ(b)] H_Z = [circ(b)^T | circ(a)^T]

n = 2m = 420 and k = 2 deg gcd(a, b, x^m - 1) = 24. The exponents of a and b are in codes/420-24-40.json under provenance.construction. To re-derive the fold bound:

python research/foldbound.py codes/420-24-40.json

Parity checks

X-checks 210 (max weight 14) · Z-checks 210 (max weight 14)
H_X (210 checks, sparse supports)
[37, 66, 78, 124, 146, 175, 186, 229, 239, 254, 263, 272, 315, 416] [38, 67, 79, 125, 147, 176, 187, 230, 240, 255, 264, 273, 316, 417] [39, 68, 80, 126, 148, 177, 188, 231, 241, 256, 265, 274, 317, 418] [40, 69, 81, 127, 149, 178, 189, 232, 242, 257, 266, 275, 318, 419] [41, 70, 82, 128, 150, 179, 190, 210, 233, 243, 258, 267, 276, 319] [42, 71, 83, 129, 151, 180, 191, 211, 234, 244, 259, 268, 277, 320] [43, 72, 84, 130, 152, 181, 192, 212, 235, 245, 260, 269, 278, 321] [44, 73, 85, 131, 153, 182, 193, 213, 236, 246, 261, 270, 279, 322] [45, 74, 86, 132, 154, 183, 194, 214, 237, 247, 262, 271, 280, 323] [46, 75, 87, 133, 155, 184, 195, 215, 238, 248, 263, 272, 281, 324] [47, 76, 88, 134, 156, 185, 196, 216, 239, 249, 264, 273, 282, 325] [48, 77, 89, 135, 157, 186, 197, 217, 240, 250, 265, 274, 283, 326] [49, 78, 90, 136, 158, 187, 198, 218, 241, 251, 266, 275, 284, 327] [50, 79, 91, 137, 159, 188, 199, 219, 242, 252, 267, 276, 285, 328] [51, 80, 92, 138, 160, 189, 200, 220, 243, 253, 268, 277, 286, 329] [52, 81, 93, 139, 161, 190, 201, 221, 244, 254, 269, 278, 287, 330] [53, 82, 94, 140, 162, 191, 202, 222, 245, 255, 270, 279, 288, 331] [54, 83, 95, 141, 163, 192, 203, 223, 246, 256, 271, 280, 289, 332] [55, 84, 96, 142, 164, 193, 204, 224, 247, 257, 272, 281, 290, 333] [56, 85, 97, 143, 165, 194, 205, 225, 248, 258, 273, 282, 291, 334] [57, 86, 98, 144, 166, 195, 206, 226, 249, 259, 274, 283, 292, 335] [58, 87, 99, 145, 167, 196, 207, 227, 250, 260, 275, 284, 293, 336] [59, 88, 100, 146, 168, 197, 208, 228, 251, 261, 276, 285, 294, 337] [60, 89, 101, 147, 169, 198, 209, 229, 252, 262, 277, 286, 295, 338] [0, 61, 90, 102, 148, 170, 199, 230, 253, 263, 278, 287, 296, 339] [1, 62, 91, 103, 149, 171, 200, 231, 254, 264, 279, 288, 297, 340] [2, 63, 92, 104, 150, 172, 201, 232, 255, 265, 280, 289, 298, 341] [3, 64, 93, 105, 151, 173, 202, 233, 256, 266, 281, 290, 299, 342] [4, 65, 94, 106, 152, 174, 203, 234, 257, 267, 282, 291, 300, 343] [5, 66, 95, 107, 153, 175, 204, 235, 258, 268, 283, 292, 301, 344] [6, 67, 96, 108, 154, 176, 205, 236, 259, 269, 284, 293, 302, 345] [7, 68, 97, 109, 155, 177, 206, 237, 260, 270, 285, 294, 303, 346] [8, 69, 98, 110, 156, 178, 207, 238, 261, 271, 286, 295, 304, 347] [9, 70, 99, 111, 157, 179, 208, 239, 262, 272, 287, 296, 305, 348] [10, 71, 100, 112, 158, 180, 209, 240, 263, 273, 288, 297, 306, 349] [0, 11, 72, 101, 113, 159, 181, 241, 264, 274, 289, 298, 307, 350] [1, 12, 73, 102, 114, 160, 182, 242, 265, 275, 290, 299, 308, 351] [2, 13, 74, 103, 115, 161, 183, 243, 266, 276, 291, 300, 309, 352] [3, 14, 75, 104, 116, 162, 184, 244, 267, 277, 292, 301, 310, 353] [4, 15, 76, 105, 117, 163, 185, 245, 268, 278, 293, 302, 311, 354] [5, 16, 77, 106, 118, 164, 186, 246, 269, 279, 294, 303, 312, 355] [6, 17, 78, 107, 119, 165, 187, 247, 270, 280, 295, 304, 313, 356] [7, 18, 79, 108, 120, 166, 188, 248, 271, 281, 296, 305, 314, 357] [8, 19, 80, 109, 121, 167, 189, 249, 272, 282, 297, 306, 315, 358] [9, 20, 81, 110, 122, 168, 190, 250, 273, 283, 298, 307, 316, 359] [10, 21, 82, 111, 123, 169, 191, 251, 274, 284, 299, 308, 317, 360] [11, 22, 83, 112, 124, 170, 192, 252, 275, 285, 300, 309, 318, 361] [12, 23, 84, 113, 125, 171, 193, 253, 276, 286, 301, 310, 319, 362] [13, 24, 85, 114, 126, 172, 194, 254, 277, 287, 302, 311, 320, 363] [14, 25, 86, 115, 127, 173, 195, 255, 278, 288, 303, 312, 321, 364] [15, 26, 87, 116, 128, 174, 196, 256, 279, 289, 304, 313, 322, 365] [16, 27, 88, 117, 129, 175, 197, 257, 280, 290, 305, 314, 323, 366] [17, 28, 89, 118, 130, 176, 198, 258, 281, 291, 306, 315, 324, 367] [18, 29, 90, 119, 131, 177, 199, 259, 282, 292, 307, 316, 325, 368] [19, 30, 91, 120, 132, 178, 200, 260, 283, 293, 308, 317, 326, 369] [20, 31, 92, 121, 133, 179, 201, 261, 284, 294, 309, 318, 327, 370] [21, 32, 93, 122, 134, 180, 202, 262, 285, 295, 310, 319, 328, 371] [22, 33, 94, 123, 135, 181, 203, 263, 286, 296, 311, 320, 329, 372] [23, 34, 95, 124, 136, 182, 204, 264, 287, 297, 312, 321, 330, 373] [24, 35, 96, 125, 137, 183, 205, 265, 288, 298, 313, 322, 331, 374] [25, 36, 97, 126, 138, 184, 206, 266, 289, 299, 314, 323, 332, 375] [26, 37, 98, 127, 139, 185, 207, 267, 290, 300, 315, 324, 333, 376] [27, 38, 99, 128, 140, 186, 208, 268, 291, 301, 316, 325, 334, 377] [28, 39, 100, 129, 141, 187, 209, 269, 292, 302, 317, 326, 335, 378] [0, 29, 40, 101, 130, 142, 188, 270, 293, 303, 318, 327, 336, 379] [1, 30, 41, 102, 131, 143, 189, 271, 294, 304, 319, 328, 337, 380] [2, 31, 42, 103, 132, 144, 190, 272, 295, 305, 320, 329, 338, 381] [3, 32, 43, 104, 133, 145, 191, 273, 296, 306, 321, 330, 339, 382] [4, 33, 44, 105, 134, 146, 192, 274, 297, 307, 322, 331, 340, 383] [5, 34, 45, 106, 135, 147, 193, 275, 298, 308, 323, 332, 341, 384] [6, 35, 46, 107, 136, 148, 194, 276, 299, 309, 324, 333, 342, 385] [7, 36, 47, 108, 137, 149, 195, 277, 300, 310, 325, 334, 343, 386] [8, 37, 48, 109, 138, 150, 196, 278, 301, 311, 326, 335, 344, 387] [9, 38, 49, 110, 139, 151, 197, 279, 302, 312, 327, 336, 345, 388] [10, 39, 50, 111, 140, 152, 198, 280, 303, 313, 328, 337, 346, 389] [11, 40, 51, 112, 141, 153, 199, 281, 304, 314, 329, 338, 347, 390] [12, 41, 52, 113, 142, 154, 200, 282, 305, 315, 330, 339, 348, 391] [13, 42, 53, 114, 143, 155, 201, 283, 306, 316, 331, 340, 349, 392] [14, 43, 54, 115, 144, 156, 202, 284, 307, 317, 332, 341, 350, 393] [15, 44, 55, 116, 145, 157, 203, 285, 308, 318, 333, 342, 351, 394] [16, 45, 56, 117, 146, 158, 204, 286, 309, 319, 334, 343, 352, 395] [17, 46, 57, 118, 147, 159, 205, 287, 310, 320, 335, 344, 353, 396] [18, 47, 58, 119, 148, 160, 206, 288, 311, 321, 336, 345, 354, 397] [19, 48, 59, 120, 149, 161, 207, 289, 312, 322, 337, 346, 355, 398] [20, 49, 60, 121, 150, 162, 208, 290, 313, 323, 338, 347, 356, 399] [21, 50, 61, 122, 151, 163, 209, 291, 314, 324, 339, 348, 357, 400] [0, 22, 51, 62, 123, 152, 164, 292, 315, 325, 340, 349, 358, 401] [1, 23, 52, 63, 124, 153, 165, 293, 316, 326, 341, 350, 359, 402] [2, 24, 53, 64, 125, 154, 166, 294, 317, 327, 342, 351, 360, 403] [3, 25, 54, 65, 126, 155, 167, 295, 318, 328, 343, 352, 361, 404] [4, 26, 55, 66, 127, 156, 168, 296, 319, 329, 344, 353, 362, 405] [5, 27, 56, 67, 128, 157, 169, 297, 320, 330, 345, 354, 363, 406] [6, 28, 57, 68, 129, 158, 170, 298, 321, 331, 346, 355, 364, 407] [7, 29, 58, 69, 130, 159, 171, 299, 322, 332, 347, 356, 365, 408] [8, 30, 59, 70, 131, 160, 172, 300, 323, 333, 348, 357, 366, 409] [9, 31, 60, 71, 132, 161, 173, 301, 324, 334, 349, 358, 367, 410] [10, 32, 61, 72, 133, 162, 174, 302, 325, 335, 350, 359, 368, 411] [11, 33, 62, 73, 134, 163, 175, 303, 326, 336, 351, 360, 369, 412] [12, 34, 63, 74, 135, 164, 176, 304, 327, 337, 352, 361, 370, 413] [13, 35, 64, 75, 136, 165, 177, 305, 328, 338, 353, 362, 371, 414] [14, 36, 65, 76, 137, 166, 178, 306, 329, 339, 354, 363, 372, 415] [15, 37, 66, 77, 138, 167, 179, 307, 330, 340, 355, 364, 373, 416] [16, 38, 67, 78, 139, 168, 180, 308, 331, 341, 356, 365, 374, 417] [17, 39, 68, 79, 140, 169, 181, 309, 332, 342, 357, 366, 375, 418] [18, 40, 69, 80, 141, 170, 182, 310, 333, 343, 358, 367, 376, 419] [19, 41, 70, 81, 142, 171, 183, 210, 311, 334, 344, 359, 368, 377] [20, 42, 71, 82, 143, 172, 184, 211, 312, 335, 345, 360, 369, 378] [21, 43, 72, 83, 144, 173, 185, 212, 313, 336, 346, 361, 370, 379] [22, 44, 73, 84, 145, 174, 186, 213, 314, 337, 347, 362, 371, 380] [23, 45, 74, 85, 146, 175, 187, 214, 315, 338, 348, 363, 372, 381] [24, 46, 75, 86, 147, 176, 188, 215, 316, 339, 349, 364, 373, 382] [25, 47, 76, 87, 148, 177, 189, 216, 317, 340, 350, 365, 374, 383] [26, 48, 77, 88, 149, 178, 190, 217, 318, 341, 351, 366, 375, 384] [27, 49, 78, 89, 150, 179, 191, 218, 319, 342, 352, 367, 376, 385] [28, 50, 79, 90, 151, 180, 192, 219, 320, 343, 353, 368, 377, 386] [29, 51, 80, 91, 152, 181, 193, 220, 321, 344, 354, 369, 378, 387] [30, 52, 81, 92, 153, 182, 194, 221, 322, 345, 355, 370, 379, 388] [31, 53, 82, 93, 154, 183, 195, 222, 323, 346, 356, 371, 380, 389] [32, 54, 83, 94, 155, 184, 196, 223, 324, 347, 357, 372, 381, 390] [33, 55, 84, 95, 156, 185, 197, 224, 325, 348, 358, 373, 382, 391] [34, 56, 85, 96, 157, 186, 198, 225, 326, 349, 359, 374, 383, 392] [35, 57, 86, 97, 158, 187, 199, 226, 327, 350, 360, 375, 384, 393] [36, 58, 87, 98, 159, 188, 200, 227, 328, 351, 361, 376, 385, 394] [37, 59, 88, 99, 160, 189, 201, 228, 329, 352, 362, 377, 386, 395] [38, 60, 89, 100, 161, 190, 202, 229, 330, 353, 363, 378, 387, 396] [39, 61, 90, 101, 162, 191, 203, 230, 331, 354, 364, 379, 388, 397] [40, 62, 91, 102, 163, 192, 204, 231, 332, 355, 365, 380, 389, 398] [41, 63, 92, 103, 164, 193, 205, 232, 333, 356, 366, 381, 390, 399] [42, 64, 93, 104, 165, 194, 206, 233, 334, 357, 367, 382, 391, 400] [43, 65, 94, 105, 166, 195, 207, 234, 335, 358, 368, 383, 392, 401] [44, 66, 95, 106, 167, 196, 208, 235, 336, 359, 369, 384, 393, 402] [45, 67, 96, 107, 168, 197, 209, 236, 337, 360, 370, 385, 394, 403] [0, 46, 68, 97, 108, 169, 198, 237, 338, 361, 371, 386, 395, 404] [1, 47, 69, 98, 109, 170, 199, 238, 339, 362, 372, 387, 396, 405] [2, 48, 70, 99, 110, 171, 200, 239, 340, 363, 373, 388, 397, 406] [3, 49, 71, 100, 111, 172, 201, 240, 341, 364, 374, 389, 398, 407] [4, 50, 72, 101, 112, 173, 202, 241, 342, 365, 375, 390, 399, 408] [5, 51, 73, 102, 113, 174, 203, 242, 343, 366, 376, 391, 400, 409] [6, 52, 74, 103, 114, 175, 204, 243, 344, 367, 377, 392, 401, 410] [7, 53, 75, 104, 115, 176, 205, 244, 345, 368, 378, 393, 402, 411] [8, 54, 76, 105, 116, 177, 206, 245, 346, 369, 379, 394, 403, 412] [9, 55, 77, 106, 117, 178, 207, 246, 347, 370, 380, 395, 404, 413] [10, 56, 78, 107, 118, 179, 208, 247, 348, 371, 381, 396, 405, 414] [11, 57, 79, 108, 119, 180, 209, 248, 349, 372, 382, 397, 406, 415] [0, 12, 58, 80, 109, 120, 181, 249, 350, 373, 383, 398, 407, 416] [1, 13, 59, 81, 110, 121, 182, 250, 351, 374, 384, 399, 408, 417] [2, 14, 60, 82, 111, 122, 183, 251, 352, 375, 385, 400, 409, 418] [3, 15, 61, 83, 112, 123, 184, 252, 353, 376, 386, 401, 410, 419] [4, 16, 62, 84, 113, 124, 185, 210, 253, 354, 377, 387, 402, 411] [5, 17, 63, 85, 114, 125, 186, 211, 254, 355, 378, 388, 403, 412] [6, 18, 64, 86, 115, 126, 187, 212, 255, 356, 379, 389, 404, 413] [7, 19, 65, 87, 116, 127, 188, 213, 256, 357, 380, 390, 405, 414] [8, 20, 66, 88, 117, 128, 189, 214, 257, 358, 381, 391, 406, 415] [9, 21, 67, 89, 118, 129, 190, 215, 258, 359, 382, 392, 407, 416] [10, 22, 68, 90, 119, 130, 191, 216, 259, 360, 383, 393, 408, 417] [11, 23, 69, 91, 120, 131, 192, 217, 260, 361, 384, 394, 409, 418] [12, 24, 70, 92, 121, 132, 193, 218, 261, 362, 385, 395, 410, 419] [13, 25, 71, 93, 122, 133, 194, 210, 219, 262, 363, 386, 396, 411] [14, 26, 72, 94, 123, 134, 195, 211, 220, 263, 364, 387, 397, 412] [15, 27, 73, 95, 124, 135, 196, 212, 221, 264, 365, 388, 398, 413] [16, 28, 74, 96, 125, 136, 197, 213, 222, 265, 366, 389, 399, 414] [17, 29, 75, 97, 126, 137, 198, 214, 223, 266, 367, 390, 400, 415] [18, 30, 76, 98, 127, 138, 199, 215, 224, 267, 368, 391, 401, 416] [19, 31, 77, 99, 128, 139, 200, 216, 225, 268, 369, 392, 402, 417] [20, 32, 78, 100, 129, 140, 201, 217, 226, 269, 370, 393, 403, 418] [21, 33, 79, 101, 130, 141, 202, 218, 227, 270, 371, 394, 404, 419] [22, 34, 80, 102, 131, 142, 203, 210, 219, 228, 271, 372, 395, 405] [23, 35, 81, 103, 132, 143, 204, 211, 220, 229, 272, 373, 396, 406] [24, 36, 82, 104, 133, 144, 205, 212, 221, 230, 273, 374, 397, 407] [25, 37, 83, 105, 134, 145, 206, 213, 222, 231, 274, 375, 398, 408] [26, 38, 84, 106, 135, 146, 207, 214, 223, 232, 275, 376, 399, 409] [27, 39, 85, 107, 136, 147, 208, 215, 224, 233, 276, 377, 400, 410] [28, 40, 86, 108, 137, 148, 209, 216, 225, 234, 277, 378, 401, 411] [0, 29, 41, 87, 109, 138, 149, 217, 226, 235, 278, 379, 402, 412] [1, 30, 42, 88, 110, 139, 150, 218, 227, 236, 279, 380, 403, 413] [2, 31, 43, 89, 111, 140, 151, 219, 228, 237, 280, 381, 404, 414] [3, 32, 44, 90, 112, 141, 152, 220, 229, 238, 281, 382, 405, 415] [4, 33, 45, 91, 113, 142, 153, 221, 230, 239, 282, 383, 406, 416] [5, 34, 46, 92, 114, 143, 154, 222, 231, 240, 283, 384, 407, 417] [6, 35, 47, 93, 115, 144, 155, 223, 232, 241, 284, 385, 408, 418] [7, 36, 48, 94, 116, 145, 156, 224, 233, 242, 285, 386, 409, 419] [8, 37, 49, 95, 117, 146, 157, 210, 225, 234, 243, 286, 387, 410] [9, 38, 50, 96, 118, 147, 158, 211, 226, 235, 244, 287, 388, 411] [10, 39, 51, 97, 119, 148, 159, 212, 227, 236, 245, 288, 389, 412] [11, 40, 52, 98, 120, 149, 160, 213, 228, 237, 246, 289, 390, 413] [12, 41, 53, 99, 121, 150, 161, 214, 229, 238, 247, 290, 391, 414] [13, 42, 54, 100, 122, 151, 162, 215, 230, 239, 248, 291, 392, 415] [14, 43, 55, 101, 123, 152, 163, 216, 231, 240, 249, 292, 393, 416] [15, 44, 56, 102, 124, 153, 164, 217, 232, 241, 250, 293, 394, 417] [16, 45, 57, 103, 125, 154, 165, 218, 233, 242, 251, 294, 395, 418] [17, 46, 58, 104, 126, 155, 166, 219, 234, 243, 252, 295, 396, 419] [18, 47, 59, 105, 127, 156, 167, 210, 220, 235, 244, 253, 296, 397] [19, 48, 60, 106, 128, 157, 168, 211, 221, 236, 245, 254, 297, 398] [20, 49, 61, 107, 129, 158, 169, 212, 222, 237, 246, 255, 298, 399] [21, 50, 62, 108, 130, 159, 170, 213, 223, 238, 247, 256, 299, 400] [22, 51, 63, 109, 131, 160, 171, 214, 224, 239, 248, 257, 300, 401] [23, 52, 64, 110, 132, 161, 172, 215, 225, 240, 249, 258, 301, 402] [24, 53, 65, 111, 133, 162, 173, 216, 226, 241, 250, 259, 302, 403] [25, 54, 66, 112, 134, 163, 174, 217, 227, 242, 251, 260, 303, 404] [26, 55, 67, 113, 135, 164, 175, 218, 228, 243, 252, 261, 304, 405] [27, 56, 68, 114, 136, 165, 176, 219, 229, 244, 253, 262, 305, 406] [28, 57, 69, 115, 137, 166, 177, 220, 230, 245, 254, 263, 306, 407] [29, 58, 70, 116, 138, 167, 178, 221, 231, 246, 255, 264, 307, 408] [30, 59, 71, 117, 139, 168, 179, 222, 232, 247, 256, 265, 308, 409] [31, 60, 72, 118, 140, 169, 180, 223, 233, 248, 257, 266, 309, 410] [32, 61, 73, 119, 141, 170, 181, 224, 234, 249, 258, 267, 310, 411] [33, 62, 74, 120, 142, 171, 182, 225, 235, 250, 259, 268, 311, 412] [34, 63, 75, 121, 143, 172, 183, 226, 236, 251, 260, 269, 312, 413] [35, 64, 76, 122, 144, 173, 184, 227, 237, 252, 261, 270, 313, 414] [36, 65, 77, 123, 145, 174, 185, 228, 238, 253, 262, 271, 314, 415]
H_Z (210 checks, sparse supports)
[4, 105, 148, 157, 166, 181, 191, 234, 245, 274, 296, 342, 354, 383] [5, 106, 149, 158, 167, 182, 192, 235, 246, 275, 297, 343, 355, 384] [6, 107, 150, 159, 168, 183, 193, 236, 247, 276, 298, 344, 356, 385] [7, 108, 151, 160, 169, 184, 194, 237, 248, 277, 299, 345, 357, 386] [8, 109, 152, 161, 170, 185, 195, 238, 249, 278, 300, 346, 358, 387] [9, 110, 153, 162, 171, 186, 196, 239, 250, 279, 301, 347, 359, 388] [10, 111, 154, 163, 172, 187, 197, 240, 251, 280, 302, 348, 360, 389] [11, 112, 155, 164, 173, 188, 198, 241, 252, 281, 303, 349, 361, 390] [12, 113, 156, 165, 174, 189, 199, 242, 253, 282, 304, 350, 362, 391] [13, 114, 157, 166, 175, 190, 200, 243, 254, 283, 305, 351, 363, 392] [14, 115, 158, 167, 176, 191, 201, 244, 255, 284, 306, 352, 364, 393] [15, 116, 159, 168, 177, 192, 202, 245, 256, 285, 307, 353, 365, 394] [16, 117, 160, 169, 178, 193, 203, 246, 257, 286, 308, 354, 366, 395] [17, 118, 161, 170, 179, 194, 204, 247, 258, 287, 309, 355, 367, 396] [18, 119, 162, 171, 180, 195, 205, 248, 259, 288, 310, 356, 368, 397] [19, 120, 163, 172, 181, 196, 206, 249, 260, 289, 311, 357, 369, 398] [20, 121, 164, 173, 182, 197, 207, 250, 261, 290, 312, 358, 370, 399] [21, 122, 165, 174, 183, 198, 208, 251, 262, 291, 313, 359, 371, 400] [22, 123, 166, 175, 184, 199, 209, 252, 263, 292, 314, 360, 372, 401] [0, 23, 124, 167, 176, 185, 200, 253, 264, 293, 315, 361, 373, 402] [1, 24, 125, 168, 177, 186, 201, 254, 265, 294, 316, 362, 374, 403] [2, 25, 126, 169, 178, 187, 202, 255, 266, 295, 317, 363, 375, 404] [3, 26, 127, 170, 179, 188, 203, 256, 267, 296, 318, 364, 376, 405] [4, 27, 128, 171, 180, 189, 204, 257, 268, 297, 319, 365, 377, 406] [5, 28, 129, 172, 181, 190, 205, 258, 269, 298, 320, 366, 378, 407] [6, 29, 130, 173, 182, 191, 206, 259, 270, 299, 321, 367, 379, 408] [7, 30, 131, 174, 183, 192, 207, 260, 271, 300, 322, 368, 380, 409] [8, 31, 132, 175, 184, 193, 208, 261, 272, 301, 323, 369, 381, 410] [9, 32, 133, 176, 185, 194, 209, 262, 273, 302, 324, 370, 382, 411] [0, 10, 33, 134, 177, 186, 195, 263, 274, 303, 325, 371, 383, 412] [1, 11, 34, 135, 178, 187, 196, 264, 275, 304, 326, 372, 384, 413] [2, 12, 35, 136, 179, 188, 197, 265, 276, 305, 327, 373, 385, 414] [3, 13, 36, 137, 180, 189, 198, 266, 277, 306, 328, 374, 386, 415] [4, 14, 37, 138, 181, 190, 199, 267, 278, 307, 329, 375, 387, 416] [5, 15, 38, 139, 182, 191, 200, 268, 279, 308, 330, 376, 388, 417] [6, 16, 39, 140, 183, 192, 201, 269, 280, 309, 331, 377, 389, 418] [7, 17, 40, 141, 184, 193, 202, 270, 281, 310, 332, 378, 390, 419] [8, 18, 41, 142, 185, 194, 203, 210, 271, 282, 311, 333, 379, 391] [9, 19, 42, 143, 186, 195, 204, 211, 272, 283, 312, 334, 380, 392] [10, 20, 43, 144, 187, 196, 205, 212, 273, 284, 313, 335, 381, 393] [11, 21, 44, 145, 188, 197, 206, 213, 274, 285, 314, 336, 382, 394] [12, 22, 45, 146, 189, 198, 207, 214, 275, 286, 315, 337, 383, 395] [13, 23, 46, 147, 190, 199, 208, 215, 276, 287, 316, 338, 384, 396] [14, 24, 47, 148, 191, 200, 209, 216, 277, 288, 317, 339, 385, 397] [0, 15, 25, 48, 149, 192, 201, 217, 278, 289, 318, 340, 386, 398] [1, 16, 26, 49, 150, 193, 202, 218, 279, 290, 319, 341, 387, 399] [2, 17, 27, 50, 151, 194, 203, 219, 280, 291, 320, 342, 388, 400] [3, 18, 28, 51, 152, 195, 204, 220, 281, 292, 321, 343, 389, 401] [4, 19, 29, 52, 153, 196, 205, 221, 282, 293, 322, 344, 390, 402] [5, 20, 30, 53, 154, 197, 206, 222, 283, 294, 323, 345, 391, 403] [6, 21, 31, 54, 155, 198, 207, 223, 284, 295, 324, 346, 392, 404] [7, 22, 32, 55, 156, 199, 208, 224, 285, 296, 325, 347, 393, 405] [8, 23, 33, 56, 157, 200, 209, 225, 286, 297, 326, 348, 394, 406] [0, 9, 24, 34, 57, 158, 201, 226, 287, 298, 327, 349, 395, 407] [1, 10, 25, 35, 58, 159, 202, 227, 288, 299, 328, 350, 396, 408] [2, 11, 26, 36, 59, 160, 203, 228, 289, 300, 329, 351, 397, 409] [3, 12, 27, 37, 60, 161, 204, 229, 290, 301, 330, 352, 398, 410] [4, 13, 28, 38, 61, 162, 205, 230, 291, 302, 331, 353, 399, 411] [5, 14, 29, 39, 62, 163, 206, 231, 292, 303, 332, 354, 400, 412] [6, 15, 30, 40, 63, 164, 207, 232, 293, 304, 333, 355, 401, 413] [7, 16, 31, 41, 64, 165, 208, 233, 294, 305, 334, 356, 402, 414] [8, 17, 32, 42, 65, 166, 209, 234, 295, 306, 335, 357, 403, 415] [0, 9, 18, 33, 43, 66, 167, 235, 296, 307, 336, 358, 404, 416] [1, 10, 19, 34, 44, 67, 168, 236, 297, 308, 337, 359, 405, 417] [2, 11, 20, 35, 45, 68, 169, 237, 298, 309, 338, 360, 406, 418] [3, 12, 21, 36, 46, 69, 170, 238, 299, 310, 339, 361, 407, 419] [4, 13, 22, 37, 47, 70, 171, 210, 239, 300, 311, 340, 362, 408] [5, 14, 23, 38, 48, 71, 172, 211, 240, 301, 312, 341, 363, 409] [6, 15, 24, 39, 49, 72, 173, 212, 241, 302, 313, 342, 364, 410] [7, 16, 25, 40, 50, 73, 174, 213, 242, 303, 314, 343, 365, 411] [8, 17, 26, 41, 51, 74, 175, 214, 243, 304, 315, 344, 366, 412] [9, 18, 27, 42, 52, 75, 176, 215, 244, 305, 316, 345, 367, 413] [10, 19, 28, 43, 53, 76, 177, 216, 245, 306, 317, 346, 368, 414] [11, 20, 29, 44, 54, 77, 178, 217, 246, 307, 318, 347, 369, 415] [12, 21, 30, 45, 55, 78, 179, 218, 247, 308, 319, 348, 370, 416] [13, 22, 31, 46, 56, 79, 180, 219, 248, 309, 320, 349, 371, 417] [14, 23, 32, 47, 57, 80, 181, 220, 249, 310, 321, 350, 372, 418] [15, 24, 33, 48, 58, 81, 182, 221, 250, 311, 322, 351, 373, 419] [16, 25, 34, 49, 59, 82, 183, 210, 222, 251, 312, 323, 352, 374] [17, 26, 35, 50, 60, 83, 184, 211, 223, 252, 313, 324, 353, 375] [18, 27, 36, 51, 61, 84, 185, 212, 224, 253, 314, 325, 354, 376] [19, 28, 37, 52, 62, 85, 186, 213, 225, 254, 315, 326, 355, 377] [20, 29, 38, 53, 63, 86, 187, 214, 226, 255, 316, 327, 356, 378] [21, 30, 39, 54, 64, 87, 188, 215, 227, 256, 317, 328, 357, 379] [22, 31, 40, 55, 65, 88, 189, 216, 228, 257, 318, 329, 358, 380] [23, 32, 41, 56, 66, 89, 190, 217, 229, 258, 319, 330, 359, 381] [24, 33, 42, 57, 67, 90, 191, 218, 230, 259, 320, 331, 360, 382] [25, 34, 43, 58, 68, 91, 192, 219, 231, 260, 321, 332, 361, 383] [26, 35, 44, 59, 69, 92, 193, 220, 232, 261, 322, 333, 362, 384] [27, 36, 45, 60, 70, 93, 194, 221, 233, 262, 323, 334, 363, 385] [28, 37, 46, 61, 71, 94, 195, 222, 234, 263, 324, 335, 364, 386] [29, 38, 47, 62, 72, 95, 196, 223, 235, 264, 325, 336, 365, 387] [30, 39, 48, 63, 73, 96, 197, 224, 236, 265, 326, 337, 366, 388] [31, 40, 49, 64, 74, 97, 198, 225, 237, 266, 327, 338, 367, 389] [32, 41, 50, 65, 75, 98, 199, 226, 238, 267, 328, 339, 368, 390] [33, 42, 51, 66, 76, 99, 200, 227, 239, 268, 329, 340, 369, 391] [34, 43, 52, 67, 77, 100, 201, 228, 240, 269, 330, 341, 370, 392] [35, 44, 53, 68, 78, 101, 202, 229, 241, 270, 331, 342, 371, 393] [36, 45, 54, 69, 79, 102, 203, 230, 242, 271, 332, 343, 372, 394] [37, 46, 55, 70, 80, 103, 204, 231, 243, 272, 333, 344, 373, 395] [38, 47, 56, 71, 81, 104, 205, 232, 244, 273, 334, 345, 374, 396] [39, 48, 57, 72, 82, 105, 206, 233, 245, 274, 335, 346, 375, 397] [40, 49, 58, 73, 83, 106, 207, 234, 246, 275, 336, 347, 376, 398] [41, 50, 59, 74, 84, 107, 208, 235, 247, 276, 337, 348, 377, 399] [42, 51, 60, 75, 85, 108, 209, 236, 248, 277, 338, 349, 378, 400] [0, 43, 52, 61, 76, 86, 109, 237, 249, 278, 339, 350, 379, 401] [1, 44, 53, 62, 77, 87, 110, 238, 250, 279, 340, 351, 380, 402] [2, 45, 54, 63, 78, 88, 111, 239, 251, 280, 341, 352, 381, 403] [3, 46, 55, 64, 79, 89, 112, 240, 252, 281, 342, 353, 382, 404] [4, 47, 56, 65, 80, 90, 113, 241, 253, 282, 343, 354, 383, 405] [5, 48, 57, 66, 81, 91, 114, 242, 254, 283, 344, 355, 384, 406] [6, 49, 58, 67, 82, 92, 115, 243, 255, 284, 345, 356, 385, 407] [7, 50, 59, 68, 83, 93, 116, 244, 256, 285, 346, 357, 386, 408] [8, 51, 60, 69, 84, 94, 117, 245, 257, 286, 347, 358, 387, 409] [9, 52, 61, 70, 85, 95, 118, 246, 258, 287, 348, 359, 388, 410] [10, 53, 62, 71, 86, 96, 119, 247, 259, 288, 349, 360, 389, 411] [11, 54, 63, 72, 87, 97, 120, 248, 260, 289, 350, 361, 390, 412] [12, 55, 64, 73, 88, 98, 121, 249, 261, 290, 351, 362, 391, 413] [13, 56, 65, 74, 89, 99, 122, 250, 262, 291, 352, 363, 392, 414] [14, 57, 66, 75, 90, 100, 123, 251, 263, 292, 353, 364, 393, 415] [15, 58, 67, 76, 91, 101, 124, 252, 264, 293, 354, 365, 394, 416] [16, 59, 68, 77, 92, 102, 125, 253, 265, 294, 355, 366, 395, 417] [17, 60, 69, 78, 93, 103, 126, 254, 266, 295, 356, 367, 396, 418] [18, 61, 70, 79, 94, 104, 127, 255, 267, 296, 357, 368, 397, 419] [19, 62, 71, 80, 95, 105, 128, 210, 256, 268, 297, 358, 369, 398] [20, 63, 72, 81, 96, 106, 129, 211, 257, 269, 298, 359, 370, 399] [21, 64, 73, 82, 97, 107, 130, 212, 258, 270, 299, 360, 371, 400] [22, 65, 74, 83, 98, 108, 131, 213, 259, 271, 300, 361, 372, 401] [23, 66, 75, 84, 99, 109, 132, 214, 260, 272, 301, 362, 373, 402] [24, 67, 76, 85, 100, 110, 133, 215, 261, 273, 302, 363, 374, 403] [25, 68, 77, 86, 101, 111, 134, 216, 262, 274, 303, 364, 375, 404] [26, 69, 78, 87, 102, 112, 135, 217, 263, 275, 304, 365, 376, 405] [27, 70, 79, 88, 103, 113, 136, 218, 264, 276, 305, 366, 377, 406] [28, 71, 80, 89, 104, 114, 137, 219, 265, 277, 306, 367, 378, 407] [29, 72, 81, 90, 105, 115, 138, 220, 266, 278, 307, 368, 379, 408] [30, 73, 82, 91, 106, 116, 139, 221, 267, 279, 308, 369, 380, 409] [31, 74, 83, 92, 107, 117, 140, 222, 268, 280, 309, 370, 381, 410] [32, 75, 84, 93, 108, 118, 141, 223, 269, 281, 310, 371, 382, 411] [33, 76, 85, 94, 109, 119, 142, 224, 270, 282, 311, 372, 383, 412] [34, 77, 86, 95, 110, 120, 143, 225, 271, 283, 312, 373, 384, 413] [35, 78, 87, 96, 111, 121, 144, 226, 272, 284, 313, 374, 385, 414] [36, 79, 88, 97, 112, 122, 145, 227, 273, 285, 314, 375, 386, 415] [37, 80, 89, 98, 113, 123, 146, 228, 274, 286, 315, 376, 387, 416] [38, 81, 90, 99, 114, 124, 147, 229, 275, 287, 316, 377, 388, 417] [39, 82, 91, 100, 115, 125, 148, 230, 276, 288, 317, 378, 389, 418] [40, 83, 92, 101, 116, 126, 149, 231, 277, 289, 318, 379, 390, 419] [41, 84, 93, 102, 117, 127, 150, 210, 232, 278, 290, 319, 380, 391] [42, 85, 94, 103, 118, 128, 151, 211, 233, 279, 291, 320, 381, 392] [43, 86, 95, 104, 119, 129, 152, 212, 234, 280, 292, 321, 382, 393] [44, 87, 96, 105, 120, 130, 153, 213, 235, 281, 293, 322, 383, 394] [45, 88, 97, 106, 121, 131, 154, 214, 236, 282, 294, 323, 384, 395] [46, 89, 98, 107, 122, 132, 155, 215, 237, 283, 295, 324, 385, 396] [47, 90, 99, 108, 123, 133, 156, 216, 238, 284, 296, 325, 386, 397] [48, 91, 100, 109, 124, 134, 157, 217, 239, 285, 297, 326, 387, 398] [49, 92, 101, 110, 125, 135, 158, 218, 240, 286, 298, 327, 388, 399] [50, 93, 102, 111, 126, 136, 159, 219, 241, 287, 299, 328, 389, 400] [51, 94, 103, 112, 127, 137, 160, 220, 242, 288, 300, 329, 390, 401] [52, 95, 104, 113, 128, 138, 161, 221, 243, 289, 301, 330, 391, 402] [53, 96, 105, 114, 129, 139, 162, 222, 244, 290, 302, 331, 392, 403] [54, 97, 106, 115, 130, 140, 163, 223, 245, 291, 303, 332, 393, 404] [55, 98, 107, 116, 131, 141, 164, 224, 246, 292, 304, 333, 394, 405] [56, 99, 108, 117, 132, 142, 165, 225, 247, 293, 305, 334, 395, 406] [57, 100, 109, 118, 133, 143, 166, 226, 248, 294, 306, 335, 396, 407] [58, 101, 110, 119, 134, 144, 167, 227, 249, 295, 307, 336, 397, 408] [59, 102, 111, 120, 135, 145, 168, 228, 250, 296, 308, 337, 398, 409] [60, 103, 112, 121, 136, 146, 169, 229, 251, 297, 309, 338, 399, 410] [61, 104, 113, 122, 137, 147, 170, 230, 252, 298, 310, 339, 400, 411] [62, 105, 114, 123, 138, 148, 171, 231, 253, 299, 311, 340, 401, 412] [63, 106, 115, 124, 139, 149, 172, 232, 254, 300, 312, 341, 402, 413] [64, 107, 116, 125, 140, 150, 173, 233, 255, 301, 313, 342, 403, 414] [65, 108, 117, 126, 141, 151, 174, 234, 256, 302, 314, 343, 404, 415] [66, 109, 118, 127, 142, 152, 175, 235, 257, 303, 315, 344, 405, 416] [67, 110, 119, 128, 143, 153, 176, 236, 258, 304, 316, 345, 406, 417] [68, 111, 120, 129, 144, 154, 177, 237, 259, 305, 317, 346, 407, 418] [69, 112, 121, 130, 145, 155, 178, 238, 260, 306, 318, 347, 408, 419] [70, 113, 122, 131, 146, 156, 179, 210, 239, 261, 307, 319, 348, 409] [71, 114, 123, 132, 147, 157, 180, 211, 240, 262, 308, 320, 349, 410] [72, 115, 124, 133, 148, 158, 181, 212, 241, 263, 309, 321, 350, 411] [73, 116, 125, 134, 149, 159, 182, 213, 242, 264, 310, 322, 351, 412] [74, 117, 126, 135, 150, 160, 183, 214, 243, 265, 311, 323, 352, 413] [75, 118, 127, 136, 151, 161, 184, 215, 244, 266, 312, 324, 353, 414] [76, 119, 128, 137, 152, 162, 185, 216, 245, 267, 313, 325, 354, 415] [77, 120, 129, 138, 153, 163, 186, 217, 246, 268, 314, 326, 355, 416] [78, 121, 130, 139, 154, 164, 187, 218, 247, 269, 315, 327, 356, 417] [79, 122, 131, 140, 155, 165, 188, 219, 248, 270, 316, 328, 357, 418] [80, 123, 132, 141, 156, 166, 189, 220, 249, 271, 317, 329, 358, 419] [81, 124, 133, 142, 157, 167, 190, 210, 221, 250, 272, 318, 330, 359] [82, 125, 134, 143, 158, 168, 191, 211, 222, 251, 273, 319, 331, 360] [83, 126, 135, 144, 159, 169, 192, 212, 223, 252, 274, 320, 332, 361] [84, 127, 136, 145, 160, 170, 193, 213, 224, 253, 275, 321, 333, 362] [85, 128, 137, 146, 161, 171, 194, 214, 225, 254, 276, 322, 334, 363] [86, 129, 138, 147, 162, 172, 195, 215, 226, 255, 277, 323, 335, 364] [87, 130, 139, 148, 163, 173, 196, 216, 227, 256, 278, 324, 336, 365] [88, 131, 140, 149, 164, 174, 197, 217, 228, 257, 279, 325, 337, 366] [89, 132, 141, 150, 165, 175, 198, 218, 229, 258, 280, 326, 338, 367] [90, 133, 142, 151, 166, 176, 199, 219, 230, 259, 281, 327, 339, 368] [91, 134, 143, 152, 167, 177, 200, 220, 231, 260, 282, 328, 340, 369] [92, 135, 144, 153, 168, 178, 201, 221, 232, 261, 283, 329, 341, 370] [93, 136, 145, 154, 169, 179, 202, 222, 233, 262, 284, 330, 342, 371] [94, 137, 146, 155, 170, 180, 203, 223, 234, 263, 285, 331, 343, 372] [95, 138, 147, 156, 171, 181, 204, 224, 235, 264, 286, 332, 344, 373] [96, 139, 148, 157, 172, 182, 205, 225, 236, 265, 287, 333, 345, 374] [97, 140, 149, 158, 173, 183, 206, 226, 237, 266, 288, 334, 346, 375] [98, 141, 150, 159, 174, 184, 207, 227, 238, 267, 289, 335, 347, 376] [99, 142, 151, 160, 175, 185, 208, 228, 239, 268, 290, 336, 348, 377] [100, 143, 152, 161, 176, 186, 209, 229, 240, 269, 291, 337, 349, 378] [0, 101, 144, 153, 162, 177, 187, 230, 241, 270, 292, 338, 350, 379] [1, 102, 145, 154, 163, 178, 188, 231, 242, 271, 293, 339, 351, 380] [2, 103, 146, 155, 164, 179, 189, 232, 243, 272, 294, 340, 352, 381] [3, 104, 147, 156, 165, 180, 190, 233, 244, 273, 295, 341, 353, 382]
Code ID 420-24-40 · download JSON · raw on GitHub