← back to the board
[[793,18,27]] d ≤
n
793
k
18
d
27
kd²/n
16.547
w
8
X/Z
1.04
g
0.0082
r
6.7082
layers
2
swaps
2711

Share this result

Distance

X/Z asymmetry 1.04 · d_X ≤ 28, 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 28 · witness weight 28 (claimed upper_bound)
witness found by @vprusso · Clifford transform + gf2_fast RIS · found at 3×108 trials · survived 1.6×107 trials · 2026-10-09
witness operator (support, 28 qubits)
[7, 10, 14, 37, 290, 311, 328, 351, 366, 368, 387, 389, 451, 466, 493, 508, 526, 529, 532, 550, 571, 586, 609, 627, 645, 648, 687, 705]
d_Z 27 · witness weight 27 (claimed upper_bound)
witness found by @dorakingx · Clifford transform + gf2_fast RIS · found at 5×106 trials · survived 1.6×107 trials · 2026-10-04
witness operator (support, 27 qubits)
[7, 10, 14, 24, 25, 32, 35, 43, 55, 78, 81, 100, 408, 411, 419, 424, 428, 430, 433, 450, 453, 458, 460, 475, 477, 479, 498]
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 7.05) · H_Z 2–8 (mean 6.928)
qubit degrees H_X 1–8 (mean 3.53) · H_Z 1–4 (mean 3.416)
trapping sets H_X (1,1)×62 (2,0)×4 (3,0)×51 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 62 (1,2): 110 (1,3): 65 (1,4): 473 (1,5): 71 (1,6): 10 (1,7): 1 (1,8): 1 (2,0): 4 (2,1): 138 (2,2): 183 (2,3): 483 (2,4): 813 (2,5): 720 (2,6): 5321 (2,7): 735 (2,8): 272 (2,9): 121 (2,10): 23 (2,11): 10 (2,12): 2 (3,0): 51 (3,1): 173 (3,2): 601 (3,3): 2195 (3,4): 3684 (3,5): 7740 (3,6): 16199 (3,7): 14144 (3,8): 85029 (3,9): 13740 (3,10): 14513 (3,11): 3817 (3,12): 2015 (3,13): 544 (3,14): 185 (3,15): 57 (3,16): 7
trapping sets H_Z (1,1)×55 (2,0)×14 (3,0)×16 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 55 (1,2): 119 (1,3): 60 (1,4): 559 (2,0): 14 (2,1): 121 (2,2): 250 (2,3): 410 (2,4): 848 (2,5): 666 (2,6): 6395 (3,0): 16 (3,1): 218 (3,2): 731 (3,3): 1833 (3,4): 3926 (3,5): 7347 (3,6): 17629 (3,7): 12533 (3,8): 103990 (3,9): 1093 (3,10): 11472
witness diameter X 20.5913 · Z 19.105 (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 = 6.708
X checkZ checkqubit site (399)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 2711 nearest-neighbor SWAPs per round in total, at most 8 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 @DennisWayo
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction One-qubit Clifford reduction of the board entry codes/794-18-27.json. The source tile construction and its prior six-qubit reduction are credited to @dorakingx; its underlying [[800,18,27]] source is credited to @e-eight. The inherited X witness is credited to @vprusso and the inherited Z witness to @dorakingx. Use source X row 0 as S={1,4,42,60,400,420,436,459} and choose a=1. Clear a from the only other incident X generator by R_287 <- R_287 + S. Apply CNOT fan-out from control 1 to targets {4,42,60,400,420,436,459}; this maps S to X_1 and maps column 1 of H_Z to zero by CSS commutation. Delete X_1 and qubit 1, then renumber every surviving source qubit q>1 as q-1. This is a Clifford equivalence followed by removal of a disentangled qubit, so k remains 18. Surviving qubits keep their source coordinates; maximum check weight remains 8, interaction radius remains 6.708203932499369, and the layout remains bilayer.
model GPT-5 (Codex) (claimed, not verified)
builds on arXiv:2504.08887
date 2026-10-11
notes Derivative contribution, not an independent tile construction. The source [[794,18,d<=27]] code and layout are credited to @dorakingx, the underlying [[800,18,27]] source to @e-eight, the transformed weight-28 X witness to @vprusso, and the transformed weight-27 Z witness to @dorakingx. The current official verifier recomputes k=18, maximum check weight 8, bilayer locality, and interaction radius 6.708203932499369. Two independent CI-style fire passes used seeds 2026101101 and 2027101104. Each pass ran the structural detector, the 50000-trial orbit-fold gate, 120160 ordinary RIS trials, and 8000000 RIS-fast trials. Neither pass found a logical below weight 27; RIS-fast reached weight 27 in both passes. Total post-reduction RIS search: 16240320 trials. Distance remains a witness-backed upper bound, not an exact-distance claim.
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

[[793,18,27]] - one-qubit reduction of [[794,18,27]]

Source and credit

This entry is a derivative of codes/794-18-27.json, not a new tile construction. The source tile code, its prior six-qubit reduction, and its bilayer layout are credited to @dorakingx; the underlying [[800,18,27]] source is credited to @e-eight. The inherited X witness is credited to @vprusso and the inherited Z witness to @dorakingx. My contribution is the additional one-qubit Clifford reduction described below.

Exact reduction

In the source numbering, take X row 0

S = {1, 4, 42, 60, 400, 420, 436, 459}

and choose a = 1. The only other X generator meeting a is source row 287, with support {1,401}. Replace it by its sum with S, so that a occurs only in S. Apply the CNOT fan-out from control 1 to targets {4,42,60,400,420,436,459}. On the binary check matrices this is

H_X[:, b] ^= H_X[:, 1]   for b in {4,42,60,400,420,436,459}
H_Z[:, 1] ^= H_Z[:, b]   for b in {4,42,60,400,420,436,459}.

The first operation maps S to the weight-one stabilizer X_1. The second maps column 1 of H_Z to the parity over S, which is zero for every Z row by CSS commutation. Qubit 1 is therefore disentangled. Delete X_1 and qubit 1, and map each surviving source index q > 1 to q - 1.

This is a Clifford equivalence followed by removal of a stabilized product qubit, hence k remains 18. Every surviving qubit keeps its source coordinate. The maximum check weight remains 8, the measured interaction radius remains 6.708203932499369, and the layout remains bilayer.

The transformed source witnesses have X weight 28 and Z weight 27 and pass the kernel and nontriviality checks. The distance claim remains an upper bound, not an exact-distance certificate.

Independent refutation

The current challenge verifier passes the schema, CSS commutation, claimed dimension, both logical witnesses, weight class, and locality checks. The candidate then survived two independent local reproductions of the current CI refutation sequence:

| pass | base seed | ordinary RIS | RIS-fast | lightest found | | --- | ---: | ---: | ---: | ---: | | A | 2026101101 | 120160 | 8000000 | 27 | | B | 2027101104 | 120160 | 8000000 | 27 |

Each pass also ran the circulant-GB detector and a 50000-trial orbit-fold stage. This tile code is not circulant GB, and the orbit stage found no applicable folded partition. Across 16240320 post-reduction RIS trials, no logical below weight 27 was found. These are strong bounded searches, not a proof of exact distance.

Board effect

The score changes from

18 * 27^2 / 794 = 16.526448

to

18 * 27^2 / 793 = 16.547289.

Thus the entry strictly dominates its [[794,18,27]] source on (n,k,d,w) while preserving the weight-8, local-2d-bilayer cell.

Tooling

The reduction search and packaging were supported by GPT-5 (Codex). Candidate generation enumerated connected row-space elements from up to three checks, enforced k=18, check weight at most 8, the source locality cap, transformed both witnesses, and admitted candidates only after the official verifier passed.

Parity checks

X-checks 397 (max weight 8) · Z-checks 391 (max weight 8)
H_X (397 checks, sparse supports)
[1, 4, 42, 60, 400, 420, 436, 459] [2, 43, 61, 401, 405, 421, 437, 460] [3, 5, 44, 62, 402, 422, 438, 461] [4, 6, 45, 63, 403, 423, 439, 462] [7, 46, 64, 404, 405, 424, 440, 463] [5, 8, 47, 65, 405, 425, 441, 464] [6, 9, 48, 66, 406, 426, 442, 465] [7, 10, 49, 67, 407, 427, 443, 466] [8, 11, 50, 68, 408, 428, 444, 467] [9, 12, 51, 69, 409, 429, 445, 468] [10, 13, 52, 70, 410, 430, 446, 469] [11, 14, 53, 71, 411, 431, 447, 470] [12, 15, 54, 72, 412, 432, 448, 471] [13, 16, 55, 73, 413, 433, 449, 472] [18, 21, 60, 78, 417, 437, 454, 477] [19, 22, 61, 79, 418, 438, 455, 478] [20, 23, 62, 80, 419, 439, 456, 479] [21, 24, 63, 81, 420, 440, 457, 480] [22, 25, 64, 82, 421, 441, 458, 481] [23, 26, 65, 83, 422, 442, 459, 482] [24, 27, 66, 84, 423, 443, 460, 483] [25, 28, 67, 85, 424, 444, 461, 484] [26, 29, 68, 86, 425, 445, 462, 485] [27, 30, 69, 87, 426, 446, 463, 486] [28, 31, 70, 88, 427, 447, 464, 487] [29, 32, 71, 89, 428, 448, 465, 488] [30, 33, 72, 90, 429, 449, 466, 489] [31, 34, 73, 91, 430, 450, 467, 490] [32, 35, 74, 92, 431, 451, 468, 491] [33, 36, 75, 93, 432, 452, 469, 492] [34, 37, 76, 94, 433, 453, 470, 493] [38, 41, 80, 98, 436, 457, 474, 497] [39, 42, 81, 99, 437, 458, 475, 498] [40, 43, 82, 100, 438, 459, 476, 499] [41, 44, 83, 101, 439, 460, 477, 500] [42, 45, 84, 102, 440, 461, 478, 501] [43, 46, 85, 103, 441, 462, 479, 502] [44, 47, 86, 104, 442, 463, 480, 503] [45, 48, 87, 105, 443, 464, 481, 504] [46, 49, 88, 106, 444, 465, 482, 505] [47, 50, 89, 107, 445, 466, 483, 506] [48, 51, 90, 108, 446, 467, 484, 507] [49, 52, 91, 109, 447, 468, 485, 508] [50, 53, 92, 110, 448, 469, 486, 509] [51, 54, 93, 111, 449, 470, 487, 510] [52, 55, 94, 112, 450, 471, 488, 511] [53, 56, 95, 113, 451, 472, 489, 512] [54, 57, 96, 114, 452, 473, 490, 513] [58, 61, 100, 118, 456, 477, 494, 517] [59, 62, 101, 119, 457, 478, 495, 518] [60, 63, 102, 120, 458, 479, 496, 519] [61, 64, 103, 121, 459, 480, 497, 520] [62, 65, 104, 122, 460, 481, 498, 521] [63, 66, 105, 123, 461, 482, 499, 522] [64, 67, 106, 124, 462, 483, 500, 523] [65, 68, 107, 125, 463, 484, 501, 524] [66, 69, 108, 126, 464, 485, 502, 525] [67, 70, 109, 127, 465, 486, 503, 526] [68, 71, 110, 128, 466, 487, 504, 527] [69, 72, 111, 129, 467, 488, 505, 528] [70, 73, 112, 130, 468, 489, 506, 529] [71, 74, 113, 131, 469, 490, 507, 530] [72, 75, 114, 132, 470, 491, 508, 531] [73, 76, 115, 133, 471, 492, 509, 532] [74, 77, 116, 134, 472, 493, 510, 533] [78, 81, 120, 138, 476, 497, 514, 537] [79, 82, 121, 139, 477, 498, 515, 538] [80, 83, 122, 140, 478, 499, 516, 539] [81, 84, 123, 141, 479, 500, 517, 540] [82, 85, 124, 142, 480, 501, 518, 541] [83, 86, 125, 143, 481, 502, 519, 542] [84, 87, 126, 144, 482, 503, 520, 543] [85, 88, 127, 145, 483, 504, 521, 544] [86, 89, 128, 146, 484, 505, 522, 545] [87, 90, 129, 147, 485, 506, 523, 546] [88, 91, 130, 148, 486, 507, 524, 547] [89, 92, 131, 149, 487, 508, 525, 548] [90, 93, 132, 150, 488, 509, 526, 549] [91, 94, 133, 151, 489, 510, 527, 550] [92, 95, 134, 152, 490, 511, 528, 551] [93, 96, 135, 153, 491, 512, 529, 552] [94, 97, 136, 154, 492, 513, 530, 553] [98, 101, 140, 158, 496, 517, 534, 557] [99, 102, 141, 159, 497, 518, 535, 558] [100, 103, 142, 160, 498, 519, 536, 559] [101, 104, 143, 161, 499, 520, 537, 560] [102, 105, 144, 162, 500, 521, 538, 561] [103, 106, 145, 163, 501, 522, 539, 562] [104, 107, 146, 164, 502, 523, 540, 563] [105, 108, 147, 165, 503, 524, 541, 564] [106, 109, 148, 166, 504, 525, 542, 565] [107, 110, 149, 167, 505, 526, 543, 566] [108, 111, 150, 168, 506, 527, 544, 567] [109, 112, 151, 169, 507, 528, 545, 568] [110, 113, 152, 170, 508, 529, 546, 569] [111, 114, 153, 171, 509, 530, 547, 570] [112, 115, 154, 172, 510, 531, 548, 571] [113, 116, 155, 173, 511, 532, 549, 572] [114, 117, 156, 174, 512, 533, 550, 573] [118, 121, 160, 178, 516, 537, 554, 577] [119, 122, 161, 179, 517, 538, 555, 578] [120, 123, 162, 180, 518, 539, 556, 579] [121, 124, 163, 181, 519, 540, 557, 580] [122, 125, 164, 182, 520, 541, 558, 581] [123, 126, 165, 183, 521, 542, 559, 582] [124, 127, 166, 184, 522, 543, 560, 583] [125, 128, 167, 185, 523, 544, 561, 584] [126, 129, 168, 186, 524, 545, 562, 585] [127, 130, 169, 187, 525, 546, 563, 586] [128, 131, 170, 188, 526, 547, 564, 587] [129, 132, 171, 189, 527, 548, 565, 588] [130, 133, 172, 190, 528, 549, 566, 589] [131, 134, 173, 191, 529, 550, 567, 590] [132, 135, 174, 192, 530, 551, 568, 591] [133, 136, 175, 193, 531, 552, 569, 592] [134, 137, 176, 194, 532, 553, 570, 593] [138, 141, 180, 198, 536, 557, 574, 596] [139, 142, 181, 199, 537, 558, 575, 597] [140, 143, 182, 200, 538, 559, 576, 598] [141, 144, 183, 201, 539, 560, 577, 599] [142, 145, 184, 202, 540, 561, 578, 600] [143, 146, 185, 203, 541, 562, 579, 601] [144, 147, 186, 204, 542, 563, 580, 602] [145, 148, 187, 205, 543, 564, 581, 603] [146, 149, 188, 206, 544, 565, 582, 604] [147, 150, 189, 207, 545, 566, 583, 605] [148, 151, 190, 208, 546, 567, 584, 606] [149, 152, 191, 209, 547, 568, 585, 607] [150, 153, 192, 210, 548, 569, 586, 608] [151, 154, 193, 211, 549, 570, 587, 609] [152, 155, 194, 212, 550, 571, 588, 610] [153, 156, 195, 213, 551, 572, 589, 611] [154, 157, 196, 214, 552, 573, 590, 612] [158, 161, 200, 218, 556, 577, 594, 616] [160, 163, 202, 220, 558, 579, 595, 618] [161, 164, 203, 221, 559, 580, 596, 619] [162, 165, 204, 222, 560, 581, 597, 620] [163, 166, 205, 223, 561, 582, 598, 621] [164, 167, 206, 224, 562, 583, 599, 622] [165, 168, 207, 225, 563, 584, 600, 623] [166, 169, 208, 226, 564, 585, 601, 624] [167, 170, 209, 227, 565, 586, 602, 625] [168, 171, 210, 228, 566, 587, 603, 626] [169, 172, 211, 229, 567, 588, 604, 627] [170, 173, 212, 230, 568, 589, 605, 628] [171, 174, 213, 231, 569, 590, 606, 629] [172, 175, 214, 232, 570, 591, 607, 630] [173, 176, 215, 233, 571, 592, 608, 631] [174, 177, 216, 234, 572, 593, 609, 632] [178, 181, 220, 238, 576, 596, 613, 636] [179, 182, 221, 239, 577, 597, 614, 637] [180, 183, 222, 240, 578, 598, 615, 638] [181, 184, 223, 241, 579, 599, 616, 639] [182, 185, 224, 242, 580, 600, 617, 640] [183, 186, 225, 243, 581, 601, 618, 641] [184, 187, 226, 244, 582, 602, 619, 642] [185, 188, 227, 245, 583, 603, 620, 643] [186, 189, 228, 246, 584, 604, 621, 644] [187, 190, 229, 247, 585, 605, 622, 645] [188, 191, 230, 248, 586, 606, 623, 646] [189, 192, 231, 249, 587, 607, 624, 647] [190, 193, 232, 250, 588, 608, 625, 648] [191, 194, 233, 251, 589, 609, 626, 649] [192, 195, 234, 252, 590, 610, 627, 650] [193, 196, 235, 253, 591, 611, 628, 651] [194, 197, 236, 254, 592, 612, 629, 652] [198, 201, 240, 258, 595, 616, 633, 656] [199, 202, 241, 259, 596, 617, 634, 657] [200, 203, 242, 260, 597, 618, 635, 658] [201, 204, 243, 261, 598, 619, 636, 659] [202, 205, 244, 262, 599, 620, 637, 660] [203, 206, 245, 263, 600, 621, 638, 661] [204, 207, 246, 264, 601, 622, 639, 662] [205, 208, 247, 265, 602, 623, 640, 663] [206, 209, 248, 266, 603, 624, 641, 664] [207, 210, 249, 267, 604, 625, 642, 665] [208, 211, 250, 268, 605, 626, 643, 666] [209, 212, 251, 269, 606, 627, 644, 667] [210, 213, 252, 270, 607, 628, 645, 668] [211, 214, 253, 271, 608, 629, 646, 669] [212, 215, 254, 272, 609, 630, 647, 670] [213, 216, 255, 273, 610, 631, 648, 671] [214, 217, 256, 274, 611, 632, 649, 672] [218, 221, 260, 278, 615, 636, 653, 676] [219, 222, 261, 279, 616, 637, 654, 677] [220, 223, 262, 280, 617, 638, 655, 678] [221, 224, 263, 281, 618, 639, 656, 679] [222, 225, 264, 282, 619, 640, 657, 680] [223, 226, 265, 283, 620, 641, 658, 681] [224, 227, 266, 284, 621, 642, 659, 682] [225, 228, 267, 285, 622, 643, 660, 683] [226, 229, 268, 286, 623, 644, 661, 684] [227, 230, 269, 287, 624, 645, 662, 685] [228, 231, 270, 288, 625, 646, 663, 686] [229, 232, 271, 289, 626, 647, 664, 687] [230, 233, 272, 290, 627, 648, 665, 688] [231, 234, 273, 291, 628, 649, 666, 689] [232, 235, 274, 292, 629, 650, 667, 690] [233, 236, 275, 293, 630, 651, 668, 691] [234, 237, 276, 294, 631, 652, 669, 692] [238, 241, 280, 298, 635, 656, 673, 696] [239, 242, 281, 299, 636, 657, 674, 697] [240, 243, 282, 300, 637, 658, 675, 698] [241, 244, 283, 301, 638, 659, 676, 699] [242, 245, 284, 302, 639, 660, 677, 700] [243, 246, 285, 303, 640, 661, 678, 701] [244, 247, 286, 304, 641, 662, 679, 702] [245, 248, 287, 305, 642, 663, 680, 703] [246, 249, 288, 306, 643, 664, 681, 704] [247, 250, 289, 307, 644, 665, 682, 705] [248, 251, 290, 308, 645, 666, 683, 706] [249, 252, 291, 309, 646, 667, 684, 707] [250, 253, 292, 310, 647, 668, 685, 708] [251, 254, 293, 311, 648, 669, 686, 709] [252, 255, 294, 312, 649, 670, 687, 710] [253, 256, 295, 313, 650, 671, 688, 711] [254, 257, 296, 314, 651, 672, 689, 712] [258, 261, 300, 318, 655, 676, 693, 716] [259, 262, 301, 319, 656, 677, 694, 717] [260, 263, 302, 320, 657, 678, 695, 718] [261, 264, 303, 321, 658, 679, 696, 719] [262, 265, 304, 322, 659, 680, 697, 720] [263, 266, 305, 323, 660, 681, 698, 721] [264, 267, 306, 324, 661, 682, 699, 722] [265, 268, 307, 325, 662, 683, 700, 723] [266, 269, 308, 326, 663, 684, 701, 724] [267, 270, 309, 327, 664, 685, 702, 725] [268, 271, 310, 328, 665, 686, 703, 726] [269, 272, 311, 329, 666, 687, 704, 727] [270, 273, 312, 330, 667, 688, 705, 728] [271, 274, 313, 331, 668, 689, 706, 729] [272, 275, 314, 332, 669, 690, 707, 730] [273, 276, 315, 333, 670, 691, 708, 731] [274, 277, 316, 334, 671, 692, 709, 732] [278, 281, 320, 338, 675, 696, 713, 736] [279, 282, 321, 339, 676, 697, 714, 737] [280, 283, 322, 340, 677, 698, 715, 738] [281, 284, 323, 341, 678, 699, 716, 739] [282, 285, 324, 342, 679, 700, 717, 740] [283, 286, 325, 343, 680, 701, 718, 741] [284, 287, 326, 344, 681, 702, 719, 742] [285, 288, 327, 345, 682, 703, 720, 743] [286, 289, 328, 346, 683, 704, 721, 744] [287, 290, 329, 347, 684, 705, 722, 745] [288, 291, 330, 348, 685, 706, 723, 746] [289, 292, 331, 349, 686, 707, 724, 747] [290, 293, 332, 350, 687, 708, 725, 748] [291, 294, 333, 351, 688, 709, 726, 749] [292, 295, 334, 352, 689, 710, 727, 750] [293, 296, 335, 353, 690, 711, 728, 751] [294, 297, 336, 354, 691, 712, 729, 752] [298, 301, 340, 358, 695, 716, 733, 756] [299, 302, 341, 359, 696, 717, 734, 757] [300, 303, 342, 360, 697, 718, 735, 758] [301, 304, 343, 361, 698, 719, 736, 759] [302, 305, 344, 362, 699, 720, 737, 760] [303, 306, 345, 363, 700, 721, 738, 761] [304, 307, 346, 364, 701, 722, 739, 762] [305, 308, 347, 365, 702, 723, 740, 763] [306, 309, 348, 366, 703, 724, 741, 764] [307, 310, 349, 367, 704, 725, 742, 765] [308, 311, 350, 368, 705, 726, 743, 766] [309, 312, 351, 369, 706, 727, 744, 767] [310, 313, 352, 370, 707, 728, 745, 768] [311, 314, 353, 371, 708, 729, 746, 769] [312, 315, 354, 372, 709, 730, 747, 770] [313, 316, 355, 373, 710, 731, 748, 771] [314, 317, 356, 374, 711, 732, 749, 772] [318, 321, 360, 378, 715, 736, 753, 776] [319, 322, 361, 379, 716, 737, 754, 777] [320, 323, 362, 380, 717, 738, 755, 778] [321, 324, 363, 381, 718, 739, 756, 779] [322, 325, 364, 382, 719, 740, 757, 780] [323, 326, 365, 383, 720, 741, 758, 781] [324, 327, 366, 384, 721, 742, 759, 782] [325, 328, 367, 385, 722, 743, 760, 783] [326, 329, 368, 386, 723, 744, 761, 784] [327, 330, 369, 387, 724, 745, 762, 785] [328, 331, 370, 388, 725, 746, 763, 786] [329, 332, 371, 389, 726, 747, 764, 787] [330, 333, 372, 390, 727, 748, 765, 788] [331, 334, 373, 391, 728, 749, 766, 789] [332, 335, 374, 392, 729, 750, 767, 790] [333, 336, 375, 393, 730, 751, 768, 791] [334, 337, 376, 394, 731, 752, 769, 792] [0, 399] [3, 41, 59, 399, 400, 419, 435, 458] [1, 401] [2, 402] [3, 403] [4, 404] [5, 406] [6, 407] [7, 408] [8, 409] [9, 410] [10, 411] [11, 412] [12, 413] [13, 414] [1, 18, 397, 418] [3, 20, 398, 420] [4, 21, 399, 421] [22, 400, 405, 422] [5, 23, 401, 423] [6, 24, 402, 424] [7, 25, 403, 425] [8, 26, 404, 426] [9, 27, 405, 427] [10, 28, 406, 428] [11, 29, 407, 429] [12, 30, 408, 430] [13, 31, 409, 431] [14, 32, 410, 432] [15, 33, 411, 433] [16, 34, 412, 434] [4, 42, 60, 400, 401, 420, 436, 459] [43, 61, 401, 402, 405, 421, 437, 460] [5, 44, 62, 402, 403, 422, 438, 461] [6, 45, 63, 403, 404, 423, 439, 462] [8, 47, 65, 405, 406, 425, 441, 464] [9, 48, 66, 406, 407, 426, 442, 465] [10, 49, 67, 407, 408, 427, 443, 466] [11, 50, 68, 408, 409, 428, 444, 467] [12, 51, 69, 409, 410, 429, 445, 468] [13, 52, 70, 410, 411, 430, 446, 469] [14, 53, 71, 411, 412, 431, 447, 470] [15, 54, 72, 412, 413, 432, 448, 471] [16, 55, 73, 413, 414, 433, 449, 472] [13, 14, 17, 56, 74, 434, 450, 473] [20, 38, 399, 415, 437] [21, 39, 400, 416, 438] [22, 40, 401, 417, 439] [23, 41, 402, 418, 440] [24, 42, 403, 419, 441] [25, 43, 404, 420, 442] [26, 44, 405, 421, 443] [27, 45, 406, 422, 444] [28, 46, 407, 423, 445] [29, 47, 408, 424, 446] [30, 48, 409, 425, 447] [31, 49, 410, 426, 448] [32, 50, 411, 427, 449] [33, 51, 412, 428, 450] [34, 52, 413, 429, 451] [35, 53, 414, 430, 452] [13, 14, 36, 54, 414, 431, 453] [338, 341, 380, 735, 756, 773] [339, 342, 381, 736, 757, 774] [340, 343, 382, 737, 758, 775] [341, 344, 383, 738, 759, 776] [342, 345, 384, 739, 760, 777] [343, 346, 385, 740, 761, 778] [344, 347, 386, 741, 762, 779] [345, 348, 387, 742, 763, 780] [346, 349, 388, 743, 764, 781] [347, 350, 389, 744, 765, 782] [348, 351, 390, 745, 766, 783] [349, 352, 391, 746, 767, 784] [350, 353, 392, 747, 768, 785] [351, 354, 393, 748, 769, 786] [353, 356, 395, 750, 771, 788] [354, 357, 396, 751, 772, 789] [358, 361, 755, 776] [359, 362, 756, 777] [360, 363, 757, 778] [361, 364, 758, 779] [362, 365, 759, 780] [363, 366, 760, 781] [364, 367, 761, 782] [365, 368, 762, 783] [366, 369, 763, 784] [367, 370, 764, 785] [368, 371, 765, 786] [369, 372, 766, 787] [370, 373, 767, 788] [371, 374, 768, 789] [372, 375, 769, 790] [373, 376, 770, 791] [374, 377, 771, 792] [378, 381, 775] [379, 382, 776] [380, 383, 777] [381, 384, 778] [382, 385, 779] [383, 386, 780] [384, 387, 781] [385, 388, 782] [386, 389, 783] [387, 390, 784] [388, 391, 785] [389, 392, 786] [390, 393, 787] [391, 394, 788] [392, 395, 789] [393, 396, 790] [352, 355, 373, 376, 394, 749, 787, 791]
H_Z (391 checks, sparse supports)
[0, 21, 38, 59, 399, 416, 454, 457] [22, 39, 60, 400, 417, 455, 458] [1, 23, 40, 61, 401, 418, 456, 459] [2, 24, 41, 62, 402, 419, 457, 460] [3, 25, 42, 63, 403, 420, 458, 461] [4, 26, 43, 64, 404, 421, 459, 462] [27, 44, 65, 405, 422, 460, 463] [5, 28, 45, 66, 406, 423, 461, 464] [6, 29, 46, 67, 407, 424, 462, 465] [7, 30, 47, 68, 408, 425, 463, 466] [8, 31, 48, 69, 409, 426, 464, 467] [9, 32, 49, 70, 410, 427, 465, 468] [10, 33, 50, 71, 411, 428, 466, 469] [11, 34, 51, 72, 412, 429, 467, 470] [12, 35, 52, 73, 413, 430, 468, 471] [13, 36, 53, 74, 414, 431, 469, 472] [14, 37, 54, 75, 432, 470, 473] [18, 41, 58, 79, 418, 435, 474, 477] [19, 42, 59, 80, 419, 436, 475, 478] [20, 43, 60, 81, 420, 437, 476, 479] [21, 44, 61, 82, 421, 438, 477, 480] [22, 45, 62, 83, 422, 439, 478, 481] [23, 46, 63, 84, 423, 440, 479, 482] [24, 47, 64, 85, 424, 441, 480, 483] [25, 48, 65, 86, 425, 442, 481, 484] [26, 49, 66, 87, 426, 443, 482, 485] [27, 50, 67, 88, 427, 444, 483, 486] [28, 51, 68, 89, 428, 445, 484, 487] [29, 52, 69, 90, 429, 446, 485, 488] [30, 53, 70, 91, 430, 447, 486, 489] [31, 54, 71, 92, 431, 448, 487, 490] [32, 55, 72, 93, 432, 449, 488, 491] [33, 56, 73, 94, 433, 450, 489, 492] [34, 57, 74, 95, 434, 451, 490, 493] [38, 61, 78, 99, 437, 455, 494, 497] [39, 62, 79, 100, 438, 456, 495, 498] [40, 63, 80, 101, 439, 457, 496, 499] [41, 64, 81, 102, 440, 458, 497, 500] [42, 65, 82, 103, 441, 459, 498, 501] [43, 66, 83, 104, 442, 460, 499, 502] [44, 67, 84, 105, 443, 461, 500, 503] [45, 68, 85, 106, 444, 462, 501, 504] [46, 69, 86, 107, 445, 463, 502, 505] [47, 70, 87, 108, 446, 464, 503, 506] [48, 71, 88, 109, 447, 465, 504, 507] [49, 72, 89, 110, 448, 466, 505, 508] [50, 73, 90, 111, 449, 467, 506, 509] [51, 74, 91, 112, 450, 468, 507, 510] [52, 75, 92, 113, 451, 469, 508, 511] [53, 76, 93, 114, 452, 470, 509, 512] [54, 77, 94, 115, 453, 471, 510, 513] [58, 81, 98, 119, 457, 475, 514, 517] [59, 82, 99, 120, 458, 476, 515, 518] [60, 83, 100, 121, 459, 477, 516, 519] [61, 84, 101, 122, 460, 478, 517, 520] [62, 85, 102, 123, 461, 479, 518, 521] [63, 86, 103, 124, 462, 480, 519, 522] [64, 87, 104, 125, 463, 481, 520, 523] [65, 88, 105, 126, 464, 482, 521, 524] [66, 89, 106, 127, 465, 483, 522, 525] [67, 90, 107, 128, 466, 484, 523, 526] [68, 91, 108, 129, 467, 485, 524, 527] [69, 92, 109, 130, 468, 486, 525, 528] [70, 93, 110, 131, 469, 487, 526, 529] [71, 94, 111, 132, 470, 488, 527, 530] [72, 95, 112, 133, 471, 489, 528, 531] [73, 96, 113, 134, 472, 490, 529, 532] [74, 97, 114, 135, 473, 491, 530, 533] [78, 101, 118, 139, 477, 495, 534, 537] [79, 102, 119, 140, 478, 496, 535, 538] [80, 103, 120, 141, 479, 497, 536, 539] [81, 104, 121, 142, 480, 498, 537, 540] [82, 105, 122, 143, 481, 499, 538, 541] [83, 106, 123, 144, 482, 500, 539, 542] [84, 107, 124, 145, 483, 501, 540, 543] [85, 108, 125, 146, 484, 502, 541, 544] [86, 109, 126, 147, 485, 503, 542, 545] [87, 110, 127, 148, 486, 504, 543, 546] [88, 111, 128, 149, 487, 505, 544, 547] [89, 112, 129, 150, 488, 506, 545, 548] [90, 113, 130, 151, 489, 507, 546, 549] [91, 114, 131, 152, 490, 508, 547, 550] [92, 115, 132, 153, 491, 509, 548, 551] [93, 116, 133, 154, 492, 510, 549, 552] [94, 117, 134, 155, 493, 511, 550, 553] [98, 121, 138, 159, 497, 515, 554, 557] [99, 122, 139, 160, 498, 516, 555, 558] [100, 123, 140, 161, 499, 517, 556, 559] [101, 124, 141, 162, 500, 518, 557, 560] [102, 125, 142, 163, 501, 519, 558, 561] [103, 126, 143, 164, 502, 520, 559, 562] [104, 127, 144, 165, 503, 521, 560, 563] [105, 128, 145, 166, 504, 522, 561, 564] [106, 129, 146, 167, 505, 523, 562, 565] [107, 130, 147, 168, 506, 524, 563, 566] [108, 131, 148, 169, 507, 525, 564, 567] [109, 132, 149, 170, 508, 526, 565, 568] [110, 133, 150, 171, 509, 527, 566, 569] [111, 134, 151, 172, 510, 528, 567, 570] [112, 135, 152, 173, 511, 529, 568, 571] [113, 136, 153, 174, 512, 530, 569, 572] [114, 137, 154, 175, 513, 531, 570, 573] [118, 141, 158, 179, 517, 535, 574, 577] [119, 142, 159, 180, 518, 536, 575, 578] [120, 143, 160, 181, 519, 537, 576, 579] [121, 144, 161, 182, 520, 538, 577, 580] [122, 145, 162, 183, 521, 539, 578, 581] [123, 146, 163, 184, 522, 540, 579, 582] [124, 147, 164, 185, 523, 541, 580, 583] [125, 148, 165, 186, 524, 542, 581, 584] [126, 149, 166, 187, 525, 543, 582, 585] [127, 150, 167, 188, 526, 544, 583, 586] [128, 151, 168, 189, 527, 545, 584, 587] [129, 152, 169, 190, 528, 546, 585, 588] [130, 153, 170, 191, 529, 547, 586, 589] [131, 154, 171, 192, 530, 548, 587, 590] [132, 155, 172, 193, 531, 549, 588, 591] [133, 156, 173, 194, 532, 550, 589, 592] [134, 157, 174, 195, 533, 551, 590, 593] [138, 161, 178, 199, 537, 555, 594, 596] [139, 162, 179, 200, 538, 556, 597] [140, 163, 180, 201, 539, 557, 595, 598] [141, 164, 181, 202, 540, 558, 596, 599] [142, 165, 182, 203, 541, 559, 597, 600] [143, 166, 183, 204, 542, 560, 598, 601] [144, 167, 184, 205, 543, 561, 599, 602] [145, 168, 185, 206, 544, 562, 600, 603] [146, 169, 186, 207, 545, 563, 601, 604] [147, 170, 187, 208, 546, 564, 602, 605] [148, 171, 188, 209, 547, 565, 603, 606] [149, 172, 189, 210, 548, 566, 604, 607] [150, 173, 190, 211, 549, 567, 605, 608] [151, 174, 191, 212, 550, 568, 606, 609] [152, 175, 192, 213, 551, 569, 607, 610] [153, 176, 193, 214, 552, 570, 608, 611] [154, 177, 194, 215, 553, 571, 609, 612] [158, 181, 198, 219, 557, 575, 613, 616] [159, 182, 199, 220, 558, 576, 614, 617] [160, 183, 200, 221, 559, 577, 615, 618] [161, 184, 201, 222, 560, 578, 616, 619] [162, 185, 202, 223, 561, 579, 617, 620] [163, 186, 203, 224, 562, 580, 618, 621] [164, 187, 204, 225, 563, 581, 619, 622] [165, 188, 205, 226, 564, 582, 620, 623] [166, 189, 206, 227, 565, 583, 621, 624] [167, 190, 207, 228, 566, 584, 622, 625] [168, 191, 208, 229, 567, 585, 623, 626] [169, 192, 209, 230, 568, 586, 624, 627] [170, 193, 210, 231, 569, 587, 625, 628] [171, 194, 211, 232, 570, 588, 626, 629] [172, 195, 212, 233, 571, 589, 627, 630] [173, 196, 213, 234, 572, 590, 628, 631] [174, 197, 214, 235, 573, 591, 629, 632] [178, 201, 218, 239, 577, 633, 636] [179, 202, 219, 240, 578, 595, 634, 637] [180, 203, 220, 241, 579, 596, 635, 638] [181, 204, 221, 242, 580, 597, 636, 639] [182, 205, 222, 243, 581, 598, 637, 640] [183, 206, 223, 244, 582, 599, 638, 641] [184, 207, 224, 245, 583, 600, 639, 642] [185, 208, 225, 246, 584, 601, 640, 643] [186, 209, 226, 247, 585, 602, 641, 644] [187, 210, 227, 248, 586, 603, 642, 645] [188, 211, 228, 249, 587, 604, 643, 646] [189, 212, 229, 250, 588, 605, 644, 647] [190, 213, 230, 251, 589, 606, 645, 648] [191, 214, 231, 252, 590, 607, 646, 649] [192, 215, 232, 253, 591, 608, 647, 650] [193, 216, 233, 254, 592, 609, 648, 651] [194, 217, 234, 255, 593, 610, 649, 652] [198, 221, 238, 259, 596, 614, 653, 656] [199, 222, 239, 260, 597, 615, 654, 657] [200, 223, 240, 261, 598, 616, 655, 658] [201, 224, 241, 262, 599, 617, 656, 659] [202, 225, 242, 263, 600, 618, 657, 660] [203, 226, 243, 264, 601, 619, 658, 661] [204, 227, 244, 265, 602, 620, 659, 662] [205, 228, 245, 266, 603, 621, 660, 663] [206, 229, 246, 267, 604, 622, 661, 664] [207, 230, 247, 268, 605, 623, 662, 665] [208, 231, 248, 269, 606, 624, 663, 666] [209, 232, 249, 270, 607, 625, 664, 667] [210, 233, 250, 271, 608, 626, 665, 668] [211, 234, 251, 272, 609, 627, 666, 669] [212, 235, 252, 273, 610, 628, 667, 670] [213, 236, 253, 274, 611, 629, 668, 671] [214, 237, 254, 275, 612, 630, 669, 672] [218, 241, 258, 279, 616, 634, 673, 676] [219, 242, 259, 280, 617, 635, 674, 677] [220, 243, 260, 281, 618, 636, 675, 678] [221, 244, 261, 282, 619, 637, 676, 679] [222, 245, 262, 283, 620, 638, 677, 680] [223, 246, 263, 284, 621, 639, 678, 681] [224, 247, 264, 285, 622, 640, 679, 682] [225, 248, 265, 286, 623, 641, 680, 683] [226, 249, 266, 287, 624, 642, 681, 684] [227, 250, 267, 288, 625, 643, 682, 685] [228, 251, 268, 289, 626, 644, 683, 686] [229, 252, 269, 290, 627, 645, 684, 687] [230, 253, 270, 291, 628, 646, 685, 688] [231, 254, 271, 292, 629, 647, 686, 689] [232, 255, 272, 293, 630, 648, 687, 690] [233, 256, 273, 294, 631, 649, 688, 691] [234, 257, 274, 295, 632, 650, 689, 692] [238, 261, 278, 299, 636, 654, 693, 696] [239, 262, 279, 300, 637, 655, 694, 697] [240, 263, 280, 301, 638, 656, 695, 698] [241, 264, 281, 302, 639, 657, 696, 699] [242, 265, 282, 303, 640, 658, 697, 700] [243, 266, 283, 304, 641, 659, 698, 701] [244, 267, 284, 305, 642, 660, 699, 702] [245, 268, 285, 306, 643, 661, 700, 703] [246, 269, 286, 307, 644, 662, 701, 704] [247, 270, 287, 308, 645, 663, 702, 705] [248, 271, 288, 309, 646, 664, 703, 706] [249, 272, 289, 310, 647, 665, 704, 707] [250, 273, 290, 311, 648, 666, 705, 708] [251, 274, 291, 312, 649, 667, 706, 709] [252, 275, 292, 313, 650, 668, 707, 710] [253, 276, 293, 314, 651, 669, 708, 711] [254, 277, 294, 315, 652, 670, 709, 712] [258, 281, 298, 319, 656, 674, 713, 716] [259, 282, 299, 320, 657, 675, 714, 717] [260, 283, 300, 321, 658, 676, 715, 718] [261, 284, 301, 322, 659, 677, 716, 719] [262, 285, 302, 323, 660, 678, 717, 720] [263, 286, 303, 324, 661, 679, 718, 721] [264, 287, 304, 325, 662, 680, 719, 722] [265, 288, 305, 326, 663, 681, 720, 723] [266, 289, 306, 327, 664, 682, 721, 724] [267, 290, 307, 328, 665, 683, 722, 725] [268, 291, 308, 329, 666, 684, 723, 726] [269, 292, 309, 330, 667, 685, 724, 727] [270, 293, 310, 331, 668, 686, 725, 728] [271, 294, 311, 332, 669, 687, 726, 729] [272, 295, 312, 333, 670, 688, 727, 730] [273, 296, 313, 334, 671, 689, 728, 731] [274, 297, 314, 335, 672, 690, 729, 732] [278, 301, 318, 339, 676, 694, 733, 736] [279, 302, 319, 340, 677, 695, 734, 737] [280, 303, 320, 341, 678, 696, 735, 738] [281, 304, 321, 342, 679, 697, 736, 739] [282, 305, 322, 343, 680, 698, 737, 740] [283, 306, 323, 344, 681, 699, 738, 741] [284, 307, 324, 345, 682, 700, 739, 742] [285, 308, 325, 346, 683, 701, 740, 743] [286, 309, 326, 347, 684, 702, 741, 744] [287, 310, 327, 348, 685, 703, 742, 745] [288, 311, 328, 349, 686, 704, 743, 746] [289, 312, 329, 350, 687, 705, 744, 747] [290, 313, 330, 351, 688, 706, 745, 748] [291, 314, 331, 352, 689, 707, 746, 749] [292, 315, 332, 353, 690, 708, 747, 750] [293, 316, 333, 354, 691, 709, 748, 751] [294, 317, 334, 355, 692, 710, 749, 752] [298, 321, 338, 359, 696, 714, 753, 756] [299, 322, 339, 360, 697, 715, 754, 757] [300, 323, 340, 361, 698, 716, 755, 758] [301, 324, 341, 362, 699, 717, 756, 759] [302, 325, 342, 363, 700, 718, 757, 760] [303, 326, 343, 364, 701, 719, 758, 761] [304, 327, 344, 365, 702, 720, 759, 762] [305, 328, 345, 366, 703, 721, 760, 763] [306, 329, 346, 367, 704, 722, 761, 764] [307, 330, 347, 368, 705, 723, 762, 765] [308, 331, 348, 369, 706, 724, 763, 766] [309, 332, 349, 370, 707, 725, 764, 767] [310, 333, 350, 371, 708, 726, 765, 768] [311, 334, 351, 372, 709, 727, 766, 769] [312, 335, 352, 373, 710, 728, 767, 770] [313, 336, 353, 374, 711, 729, 768, 771] [314, 337, 354, 375, 712, 730, 769, 772] [318, 341, 358, 379, 716, 734, 773, 776] [319, 342, 359, 380, 717, 735, 774, 777] [320, 343, 360, 381, 718, 736, 775, 778] [321, 344, 361, 382, 719, 737, 776, 779] [322, 345, 362, 383, 720, 738, 777, 780] [323, 346, 363, 384, 721, 739, 778, 781] [324, 347, 364, 385, 722, 740, 779, 782] [325, 348, 365, 386, 723, 741, 780, 783] [326, 349, 366, 387, 724, 742, 781, 784] [327, 350, 367, 388, 725, 743, 782, 785] [328, 351, 368, 389, 726, 744, 783, 786] [329, 352, 369, 390, 727, 745, 784, 787] [330, 353, 370, 391, 728, 746, 785, 788] [331, 354, 371, 392, 729, 747, 786, 789] [332, 355, 372, 393, 730, 748, 787, 790] [333, 356, 373, 394, 731, 749, 788, 791] [334, 357, 374, 395, 732, 750, 789, 792] [18, 397, 454] [38, 415, 474] [58, 494] [78, 454, 514] [98, 474, 534] [118, 494, 554] [138, 514, 574] [158, 534, 594] [178, 554, 613] [198, 574, 633] [218, 594, 653] [238, 613, 673] [258, 633, 693] [278, 653, 713] [298, 673, 733] [318, 693, 753] [338, 713, 773] [19, 455] [39, 416, 475] [59, 435, 495] [79, 455, 515] [99, 475, 535] [119, 495, 555] [139, 515, 575] [159, 535] [179, 555, 614] [199, 575, 634] [219, 654] [239, 614, 674] [259, 634, 694] [279, 654, 714] [299, 674, 734] [319, 694, 754] [339, 714, 774] [20, 58, 398, 415, 456] [40, 78, 417, 476] [60, 98, 436, 454, 496] [80, 118, 456, 474, 516] [100, 138, 476, 494, 536] [120, 158, 496, 514, 556] [140, 178, 516, 534, 576] [160, 198, 536, 554, 595] [180, 218, 556, 574, 615] [200, 238, 576, 594, 635] [220, 258, 595, 613, 655] [240, 278, 615, 633, 675] [260, 298, 635, 653, 695] [280, 318, 655, 673, 715] [300, 338, 675, 693, 735] [320, 358, 695, 713, 755] [340, 378, 715, 733, 775] [16, 56, 77, 434, 472] [36, 76, 97, 453, 492] [56, 96, 117, 473, 512] [76, 116, 137, 493, 532] [96, 136, 157, 513, 552] [116, 156, 177, 533, 572] [136, 176, 197, 553, 592] [156, 196, 217, 573, 611] [176, 216, 237, 593, 631] [196, 236, 257, 612, 651] [216, 256, 277, 632, 671] [236, 276, 297, 652, 691] [256, 296, 317, 672, 711] [276, 316, 337, 692, 731] [296, 336, 357, 712, 751] [316, 356, 377, 732, 771] [336, 376, 752, 791] [15, 55, 76, 433, 471] [35, 75, 96, 452, 491] [55, 95, 116, 472, 511] [75, 115, 136, 492, 531] [95, 135, 156, 512, 551] [115, 155, 176, 532, 571] [135, 175, 196, 552, 591] [155, 195, 216, 572, 610] [175, 215, 236, 592, 630] [195, 235, 256, 611, 650] [215, 255, 276, 631, 670] [235, 275, 296, 651, 690] [255, 295, 316, 671, 710] [275, 315, 336, 691, 730] [295, 335, 356, 711, 750] [315, 355, 376, 731, 770] [335, 375, 396, 751, 790] [17, 57, 473] [37, 77, 493] [57, 97, 513] [77, 117, 533] [97, 137, 553] [117, 157, 573] [137, 177, 593] [157, 197, 612] [177, 217, 632] [197, 237, 652] [217, 257, 672] [237, 277, 692] [257, 297, 712] [277, 317, 732] [297, 337, 752] [317, 357, 772] [337, 377, 792]
Code ID 793-18-27 · download JSON · raw on GitHub