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[[921,18,31]] d ≤
n
921
k
18
d
31
kd²/n
18.782
w
8
X/Z
1
g
0.058
r
4.2426
layers
2
swaps
3186

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Distance

X/Z asymmetry 1 · d_X ≤ 31, d_Z ≤ 31 · 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 31 · witness weight 31 (claimed upper_bound)
witness found by @dorakingx · Clifford transform + gf2_fast RIS · found at 2×107 trials · survived 1.6×107 trials · 2026-09-17
witness operator (support, 31 qubits)
[30, 42, 341, 364, 383, 408, 425, 427, 448, 450, 470, 481, 482, 496, 525, 542, 559, 588, 605, 625, 628, 631, 651, 674, 691, 717, 736, 756, 759, 802, 822]
d_Z 31 · witness weight 31 (claimed upper_bound)
witness found by @vprusso · Clifford transform + gf2_fast RIS · found at 3×108 trials · survived 1.6×107 trials · 2026-09-25
witness operator (support, 31 qubits)
[109, 172, 192, 212, 218, 232, 235, 252, 258, 264, 275, 281, 287, 312, 315, 318, 321, 324, 327, 330, 332, 353, 660, 685, 710, 728, 749, 751, 772, 793, 814]
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 7.051) · H_Z 2–8 (mean 7.024)
qubit degrees H_X 1–6 (mean 3.606) · H_Z 1–4 (mean 3.432)
trapping sets H_X (1,1)×63 (2,0)×3 (3,0)×54 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 63 (1,2): 117 (1,3): 65 (1,4): 566 (1,5): 95 (1,6): 15 (2,0): 3 (2,1): 147 (2,2): 188 (2,3): 496 (2,4): 866 (2,5): 717 (2,6): 6583 (2,7): 860 (2,8): 389 (2,9): 179 (2,10): 13 (3,0): 54 (3,1): 182 (3,2): 614 (3,3): 2274 (3,4): 3801 (3,5): 8027 (3,6): 17769 (3,7): 14229 (3,8): 107065 (3,9): 16272 (3,10): 18784 (3,11): 4879 (3,12): 2754 (3,13): 598 (3,14): 61
trapping sets H_Z (1,1)×65 (2,0)×18 (3,0)×19 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 65 (1,2): 131 (1,3): 66 (1,4): 659 (2,0): 18 (2,1): 140 (2,2): 281 (2,3): 463 (2,4): 940 (2,5): 738 (2,6): 7667 (3,0): 19 (3,1): 259 (3,2): 845 (3,3): 2102 (3,4): 4440 (3,5): 8316 (3,6): 20023 (3,7): 13992 (3,8): 126567 (3,9): 1217 (3,10): 13894
witness diameter X 23.3238 · Z 23.7065 (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 (462)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 3186 nearest-neighbor SWAPs per round in total, at most 5 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/922-18-31.json. The source [[922,18,31]] reduction is credited to @dorakingx and its underlying [[924,18,31]] tile code to @e-eight. The inherited X witness is credited to @dorakingx and the inherited Z witness to @vprusso. In source numbering, use X row 359 as the weight-two stabilizer S={18,483} and choose a=483. Clear a from the other incident X generators by R_396 <- R_396 + S and R_415 <- R_415 + S. Apply CNOT fan-out from control 483 to target 18; this maps S to X_483 and maps column 483 of H_Z to zero by CSS commutation. Delete X_483 and qubit 483, then renumber every surviving source qubit q>483 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 4.242640687119285, 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 [[922,18,d<=31]] reduction is credited to @dorakingx, the underlying [[924,18,31]] tile construction to @e-eight, the transformed weight-31 X witness to @dorakingx, and the transformed weight-31 Z witness to @vprusso. The current official verifier recomputes k=18, maximum check weight 8, bilayer locality, and interaction radius 4.242640687119285. Two independent CI-style fire passes used base seeds 2026101111 and 2027101114. Each pass ran the structural detectors, ordinary RIS, and 8000000 RIS-fast trials. Neither pass found a logical below weight 31; RIS-fast reached weight 31 in both passes. Total post-reduction RIS search: 16078680 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

[[921,18,31]] - one-qubit reduction of [[922,18,31]]

Source and credit

This entry is a derivative of codes/922-18-31.json, not a new tile construction. The source [[922,18,31]] reduction and its bilayer layout are credited to @dorakingx; the underlying [[924,18,31]] tile code is credited to @e-eight. The inherited X witness is credited to @dorakingx and the inherited Z witness to @vprusso. My contribution is the additional one-qubit Clifford reduction described below.

Exact reduction

In the source numbering, X row 359 is the weight-two stabilizer

S = {18, 483}.

Choose a = 483. The two other X generators meeting a are source rows 396 and 415. Clear a from them by

R_396 <- R_396 + S
R_415 <- R_415 + S.

Their supports become {18,21,64,84,482,504,523,548} and {18,42,62,501,526}, respectively. Apply the CNOT with control 483 and target 18. On the binary check matrices this is

H_X[:, 18]  ^= H_X[:, 483]
H_Z[:, 483] ^= H_Z[:, 18].

The first operation maps S to the weight-one stabilizer X_483. The second maps column 483 of H_Z to the parity over S, which is zero for every Z row by CSS commutation. In the explicit source matrix, Z row 18 is the only Z row meeting qubit 483 and it contains both 18 and 483, so the column clears directly. Qubit 483 is therefore disentangled. Delete X_483 and qubit 483, and map each surviving source index q > 483 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 4.242640687119285, and the layout remains bilayer.

The transformed source witnesses both have weight 31 and pass the kernel and nontriviality checks. The distance claim remains an upper bound, not an exact distance certificate.

Independent refutation

The candidate survived two independent local reproductions of the current CI refutation sequence:

| pass | base seed | ordinary RIS | RIS-fast | lightest found | | --- | ---: | ---: | ---: | ---: | | A | 2026101111 | 39340 | 8000000 | 31 | | B | 2027101114 | 39340 | 8000000 | 31 |

Each pass also ran the circulant-GB and orbit-fold structural detectors; this tile code supplied no applicable structural partition. Across 16078680 post-reduction RIS trials, no logical below weight 31 was found. These are strong bounded searches, not a proof of exact distance.

Board effect

The score changes from

18 * 31^2 / 922 = 18.761388

to

18 * 31^2 / 921 = 18.781759.

Thus the entry strictly improves its [[922,18,31]] source by block length while preserving k, the witness-backed distance claim, weight 8, and the local-2d-bilayer class.

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 471 (max weight 8) · Z-checks 450 (max weight 8)
H_X (471 checks, sparse supports)
[0, 3, 46, 66, 464, 485, 504, 529] [1, 4, 47, 67, 465, 486, 505, 530] [2, 5, 48, 68, 466, 487, 506, 531] [3, 6, 49, 69, 467, 488, 507, 532] [4, 7, 50, 70, 468, 489, 508, 533] [5, 8, 51, 71, 469, 490, 509, 534] [6, 9, 52, 72, 470, 491, 510, 535] [7, 10, 53, 73, 471, 492, 511, 536] [8, 11, 54, 74, 472, 493, 512, 537] [9, 12, 55, 75, 473, 494, 513, 538] [10, 13, 56, 76, 474, 495, 514, 539] [11, 14, 57, 77, 475, 496, 515, 540] [12, 15, 58, 78, 476, 497, 516, 541] [13, 16, 59, 79, 477, 498, 517, 542] [14, 17, 60, 80, 478, 499, 518, 543] [15, 18, 61, 81, 479, 500, 519, 544] [16, 19, 62, 82, 480, 501, 520, 545] [17, 20, 63, 83, 481, 502, 521, 546] [18, 21, 64, 84, 482, 503, 522, 547] [22, 25, 68, 88, 484, 507, 526, 551] [23, 26, 69, 89, 485, 508, 527, 552] [24, 27, 70, 90, 486, 509, 528, 553] [25, 28, 71, 91, 487, 510, 529, 554] [26, 29, 72, 92, 488, 511, 530, 555] [27, 30, 73, 93, 489, 512, 531, 556] [28, 31, 74, 94, 490, 513, 532, 557] [29, 32, 75, 95, 491, 514, 533, 558] [30, 33, 76, 96, 492, 515, 534, 559] [31, 34, 77, 97, 493, 516, 535, 560] [32, 35, 78, 98, 494, 517, 536, 561] [33, 36, 79, 99, 495, 518, 537, 562] [34, 37, 80, 100, 496, 519, 538, 563] [35, 38, 81, 101, 497, 520, 539, 564] [36, 39, 82, 102, 498, 521, 540, 565] [37, 40, 83, 103, 499, 522, 541, 566] [38, 41, 84, 104, 500, 523, 542, 567] [39, 42, 85, 105, 501, 524, 543, 568] [40, 43, 86, 106, 502, 525, 544, 569] [44, 47, 90, 110, 506, 529, 548, 573] [45, 48, 91, 111, 507, 530, 549, 574] [46, 49, 92, 112, 508, 531, 550, 575] [47, 50, 93, 113, 509, 532, 551, 576] [48, 51, 94, 114, 510, 533, 552, 577] [49, 52, 95, 115, 511, 534, 553, 578] [50, 53, 96, 116, 512, 535, 554, 579] [51, 54, 97, 117, 513, 536, 555, 580] [52, 55, 98, 118, 514, 537, 556, 581] [53, 56, 99, 119, 515, 538, 557, 582] [54, 57, 100, 120, 516, 539, 558, 583] [55, 58, 101, 121, 517, 540, 559, 584] [56, 59, 102, 122, 518, 541, 560, 585] [57, 60, 103, 123, 519, 542, 561, 586] [58, 61, 104, 124, 520, 543, 562, 587] [59, 62, 105, 125, 521, 544, 563, 588] [60, 63, 106, 126, 522, 545, 564, 589] [61, 64, 107, 127, 523, 546, 565, 590] [62, 65, 108, 128, 524, 547, 566, 591] [66, 69, 112, 132, 528, 551, 570, 595] [67, 70, 113, 133, 529, 552, 571, 596] [68, 71, 114, 134, 530, 553, 572, 597] [69, 72, 115, 135, 531, 554, 573, 598] [70, 73, 116, 136, 532, 555, 574, 599] [71, 74, 117, 137, 533, 556, 575, 600] [72, 75, 118, 138, 534, 557, 576, 601] [73, 76, 119, 139, 535, 558, 577, 602] [74, 77, 120, 140, 536, 559, 578, 603] [75, 78, 121, 141, 537, 560, 579, 604] [76, 79, 122, 142, 538, 561, 580, 605] [77, 80, 123, 143, 539, 562, 581, 606] [78, 81, 124, 144, 540, 563, 582, 607] [79, 82, 125, 145, 541, 564, 583, 608] [80, 83, 126, 146, 542, 565, 584, 609] [81, 84, 127, 147, 543, 566, 585, 610] [82, 85, 128, 148, 544, 567, 586, 611] [83, 86, 129, 149, 545, 568, 587, 612] [84, 87, 130, 150, 546, 569, 588, 613] [88, 91, 134, 154, 550, 573, 592, 617] [89, 92, 135, 155, 551, 574, 593, 618] [90, 93, 136, 156, 552, 575, 594, 619] [91, 94, 137, 157, 553, 576, 595, 620] [92, 95, 138, 158, 554, 577, 596, 621] [93, 96, 139, 159, 555, 578, 597, 622] [94, 97, 140, 160, 556, 579, 598, 623] [95, 98, 141, 161, 557, 580, 599, 624] [96, 99, 142, 162, 558, 581, 600, 625] [97, 100, 143, 163, 559, 582, 601, 626] [98, 101, 144, 164, 560, 583, 602, 627] [99, 102, 145, 165, 561, 584, 603, 628] [100, 103, 146, 166, 562, 585, 604, 629] [101, 104, 147, 167, 563, 586, 605, 630] [102, 105, 148, 168, 564, 587, 606, 631] [103, 106, 149, 169, 565, 588, 607, 632] [104, 107, 150, 170, 566, 589, 608, 633] [105, 108, 151, 171, 567, 590, 609, 634] [106, 109, 152, 172, 568, 591, 610, 635] [110, 113, 156, 176, 572, 595, 614, 639] [111, 114, 157, 177, 573, 596, 615, 640] [112, 115, 158, 178, 574, 597, 616, 641] [113, 116, 159, 179, 575, 598, 617, 642] [114, 117, 160, 180, 576, 599, 618, 643] [115, 118, 161, 181, 577, 600, 619, 644] [116, 119, 162, 182, 578, 601, 620, 645] [117, 120, 163, 183, 579, 602, 621, 646] [118, 121, 164, 184, 580, 603, 622, 647] [119, 122, 165, 185, 581, 604, 623, 648] [120, 123, 166, 186, 582, 605, 624, 649] [121, 124, 167, 187, 583, 606, 625, 650] [122, 125, 168, 188, 584, 607, 626, 651] [123, 126, 169, 189, 585, 608, 627, 652] [124, 127, 170, 190, 586, 609, 628, 653] [125, 128, 171, 191, 587, 610, 629, 654] [126, 129, 172, 192, 588, 611, 630, 655] [127, 130, 173, 193, 589, 612, 631, 656] [128, 131, 174, 194, 590, 613, 632, 657] [132, 135, 178, 198, 594, 617, 636, 661] [133, 136, 179, 199, 595, 618, 637, 662] [134, 137, 180, 200, 596, 619, 638, 663] [135, 138, 181, 201, 597, 620, 639, 664] [136, 139, 182, 202, 598, 621, 640, 665] [137, 140, 183, 203, 599, 622, 641, 666] [138, 141, 184, 204, 600, 623, 642, 667] [139, 142, 185, 205, 601, 624, 643, 668] [140, 143, 186, 206, 602, 625, 644, 669] [141, 144, 187, 207, 603, 626, 645, 670] [142, 145, 188, 208, 604, 627, 646, 671] [143, 146, 189, 209, 605, 628, 647, 672] [144, 147, 190, 210, 606, 629, 648, 673] [145, 148, 191, 211, 607, 630, 649, 674] [146, 149, 192, 212, 608, 631, 650, 675] [147, 150, 193, 213, 609, 632, 651, 676] [148, 151, 194, 214, 610, 633, 652, 677] [149, 152, 195, 215, 611, 634, 653, 678] [150, 153, 196, 216, 612, 635, 654, 679] [154, 157, 200, 220, 616, 639, 658, 683] [155, 158, 201, 221, 617, 640, 659, 684] [156, 159, 202, 222, 618, 641, 660, 685] [157, 160, 203, 223, 619, 642, 661, 686] [158, 161, 204, 224, 620, 643, 662, 687] [159, 162, 205, 225, 621, 644, 663, 688] [160, 163, 206, 226, 622, 645, 664, 689] [161, 164, 207, 227, 623, 646, 665, 690] [162, 165, 208, 228, 624, 647, 666, 691] [163, 166, 209, 229, 625, 648, 667, 692] [164, 167, 210, 230, 626, 649, 668, 693] [165, 168, 211, 231, 627, 650, 669, 694] [166, 169, 212, 232, 628, 651, 670, 695] [167, 170, 213, 233, 629, 652, 671, 696] [168, 171, 214, 234, 630, 653, 672, 697] [169, 172, 215, 235, 631, 654, 673, 698] [170, 173, 216, 236, 632, 655, 674, 699] [171, 174, 217, 237, 633, 656, 675, 700] [172, 175, 218, 238, 634, 657, 676, 701] [176, 179, 222, 242, 638, 661, 680, 705] [177, 180, 223, 243, 639, 662, 681, 706] [178, 181, 224, 244, 640, 663, 682, 707] [179, 182, 225, 245, 641, 664, 683, 708] [180, 183, 226, 246, 642, 665, 684, 709] [181, 184, 227, 247, 643, 666, 685, 710] [182, 185, 228, 248, 644, 667, 686, 711] [183, 186, 229, 249, 645, 668, 687, 712] [184, 187, 230, 250, 646, 669, 688, 713] [185, 188, 231, 251, 647, 670, 689, 714] [186, 189, 232, 252, 648, 671, 690, 715] [187, 190, 233, 253, 649, 672, 691, 716] [188, 191, 234, 254, 650, 673, 692, 717] [189, 192, 235, 255, 651, 674, 693, 718] [190, 193, 236, 256, 652, 675, 694, 719] [191, 194, 237, 257, 653, 676, 695, 720] [192, 195, 238, 258, 654, 677, 696, 721] [193, 196, 239, 259, 655, 678, 697, 722] [194, 197, 240, 260, 656, 679, 698, 723] [198, 201, 244, 264, 660, 683, 702, 726] [199, 202, 245, 265, 661, 684, 703, 727] [200, 203, 246, 266, 662, 685, 704, 728] [201, 204, 247, 267, 663, 686, 705, 729] [202, 205, 248, 268, 664, 687, 706, 730] [203, 206, 249, 269, 665, 688, 707, 731] [204, 207, 250, 270, 666, 689, 708, 732] [205, 208, 251, 271, 667, 690, 709, 733] [206, 209, 252, 272, 668, 691, 710, 734] [207, 210, 253, 273, 669, 692, 711, 735] [208, 211, 254, 274, 670, 693, 712, 736] [209, 212, 255, 275, 671, 694, 713, 737] [210, 213, 256, 276, 672, 695, 714, 738] [211, 214, 257, 277, 673, 696, 715, 739] [212, 215, 258, 278, 674, 697, 716, 740] [213, 216, 259, 279, 675, 698, 717, 741] [214, 217, 260, 280, 676, 699, 718, 742] [215, 218, 261, 281, 677, 700, 719, 743] [216, 219, 262, 282, 678, 701, 720, 744] [221, 224, 267, 287, 683, 706, 724, 749] [222, 225, 268, 288, 684, 707, 725, 750] [223, 226, 269, 289, 685, 708, 726, 751] [224, 227, 270, 290, 686, 709, 727, 752] [225, 228, 271, 291, 687, 710, 728, 753] [226, 229, 272, 292, 688, 711, 729, 754] [227, 230, 273, 293, 689, 712, 730, 755] [228, 231, 274, 294, 690, 713, 731, 756] [229, 232, 275, 295, 691, 714, 732, 757] [230, 233, 276, 296, 692, 715, 733, 758] [231, 234, 277, 297, 693, 716, 734, 759] [232, 235, 278, 298, 694, 717, 735, 760] [233, 236, 279, 299, 695, 718, 736, 761] [234, 237, 280, 300, 696, 719, 737, 762] [235, 238, 281, 301, 697, 720, 738, 763] [236, 239, 282, 302, 698, 721, 739, 764] [237, 240, 283, 303, 699, 722, 740, 765] [238, 241, 284, 304, 700, 723, 741, 766] [242, 245, 288, 308, 704, 726, 745, 770] [243, 246, 289, 309, 705, 727, 746, 771] [244, 247, 290, 310, 706, 728, 747, 772] [245, 248, 291, 311, 707, 729, 748, 773] [246, 249, 292, 312, 708, 730, 749, 774] [247, 250, 293, 313, 709, 731, 750, 775] [248, 251, 294, 314, 710, 732, 751, 776] [249, 252, 295, 315, 711, 733, 752, 777] [250, 253, 296, 316, 712, 734, 753, 778] [251, 254, 297, 317, 713, 735, 754, 779] [252, 255, 298, 318, 714, 736, 755, 780] [253, 256, 299, 319, 715, 737, 756, 781] [254, 257, 300, 320, 716, 738, 757, 782] [255, 258, 301, 321, 717, 739, 758, 783] [256, 259, 302, 322, 718, 740, 759, 784] [257, 260, 303, 323, 719, 741, 760, 785] [258, 261, 304, 324, 720, 742, 761, 786] [259, 262, 305, 325, 721, 743, 762, 787] [260, 263, 306, 326, 722, 744, 763, 788] [264, 267, 310, 330, 725, 748, 767, 792] [265, 268, 311, 331, 726, 749, 768, 793] [266, 269, 312, 332, 727, 750, 769, 794] [267, 270, 313, 333, 728, 751, 770, 795] [268, 271, 314, 334, 729, 752, 771, 796] [269, 272, 315, 335, 730, 753, 772, 797] [270, 273, 316, 336, 731, 754, 773, 798] [271, 274, 317, 337, 732, 755, 774, 799] [272, 275, 318, 338, 733, 756, 775, 800] [273, 276, 319, 339, 734, 757, 776, 801] [274, 277, 320, 340, 735, 758, 777, 802] [275, 278, 321, 341, 736, 759, 778, 803] [276, 279, 322, 342, 737, 760, 779, 804] [277, 280, 323, 343, 738, 761, 780, 805] [278, 281, 324, 344, 739, 762, 781, 806] [279, 282, 325, 345, 740, 763, 782, 807] [280, 283, 326, 346, 741, 764, 783, 808] [281, 284, 327, 347, 742, 765, 784, 809] [282, 285, 328, 348, 743, 766, 785, 810] [286, 289, 332, 352, 747, 770, 789, 814] [287, 290, 333, 353, 748, 771, 790, 815] [288, 291, 334, 354, 749, 772, 791, 816] [289, 292, 335, 355, 750, 773, 792, 817] [290, 293, 336, 356, 751, 774, 793, 818] [291, 294, 337, 357, 752, 775, 794, 819] [292, 295, 338, 358, 753, 776, 795, 820] [293, 296, 339, 359, 754, 777, 796, 821] [294, 297, 340, 360, 755, 778, 797, 822] [295, 298, 341, 361, 756, 779, 798, 823] [296, 299, 342, 362, 757, 780, 799, 824] [297, 300, 343, 363, 758, 781, 800, 825] [298, 301, 344, 364, 759, 782, 801, 826] [299, 302, 345, 365, 760, 783, 802, 827] [300, 303, 346, 366, 761, 784, 803, 828] [301, 304, 347, 367, 762, 785, 804, 829] [302, 305, 348, 368, 763, 786, 805, 830] [303, 306, 349, 369, 764, 787, 806, 831] [304, 307, 350, 370, 765, 788, 807, 832] [308, 311, 354, 374, 769, 792, 811, 836] [309, 312, 355, 375, 770, 793, 812, 837] [310, 313, 356, 376, 771, 794, 813, 838] [311, 314, 357, 377, 772, 795, 814, 839] [312, 315, 358, 378, 773, 796, 815, 840] [313, 316, 359, 379, 774, 797, 816, 841] [314, 317, 360, 380, 775, 798, 817, 842] [315, 318, 361, 381, 776, 799, 818, 843] [316, 319, 362, 382, 777, 800, 819, 844] [317, 320, 363, 383, 778, 801, 820, 845] [318, 321, 364, 384, 779, 802, 821, 846] [319, 322, 365, 385, 780, 803, 822, 847] [320, 323, 366, 386, 781, 804, 823, 848] [321, 324, 367, 387, 782, 805, 824, 849] [322, 325, 368, 388, 783, 806, 825, 850] [323, 326, 369, 389, 784, 807, 826, 851] [324, 327, 370, 390, 785, 808, 827, 852] [325, 328, 371, 391, 786, 809, 828, 853] [326, 329, 372, 392, 787, 810, 829, 854] [330, 333, 376, 396, 791, 814, 833, 858] [331, 334, 377, 397, 792, 815, 834, 859] [332, 335, 378, 398, 793, 816, 835, 860] [333, 336, 379, 399, 794, 817, 836, 861] [334, 337, 380, 400, 795, 818, 837, 862] [335, 338, 381, 401, 796, 819, 838, 863] [336, 339, 382, 402, 797, 820, 839, 864] [337, 340, 383, 403, 798, 821, 840, 865] [338, 341, 384, 404, 799, 822, 841, 866] [339, 342, 385, 405, 800, 823, 842, 867] [340, 343, 386, 406, 801, 824, 843, 868] [341, 344, 387, 407, 802, 825, 844, 869] [342, 345, 388, 408, 803, 826, 845, 870] [343, 346, 389, 409, 804, 827, 846, 871] [344, 347, 390, 410, 805, 828, 847, 872] [345, 348, 391, 411, 806, 829, 848, 873] [346, 349, 392, 412, 807, 830, 849, 874] [347, 350, 393, 413, 808, 831, 850, 875] [348, 351, 394, 414, 809, 832, 851, 876] [352, 355, 398, 418, 813, 836, 855, 880] [353, 356, 399, 419, 814, 837, 856, 881] [354, 357, 400, 420, 815, 838, 857, 882] [355, 358, 401, 421, 816, 839, 858, 883] [356, 359, 402, 422, 817, 840, 859, 884] [357, 360, 403, 423, 818, 841, 860, 885] [358, 361, 404, 424, 819, 842, 861, 886] [359, 362, 405, 425, 820, 843, 862, 887] [360, 363, 406, 426, 821, 844, 863, 888] [361, 364, 407, 427, 822, 845, 864, 889] [362, 365, 408, 428, 823, 846, 865, 890] [363, 366, 409, 429, 824, 847, 866, 891] [364, 367, 410, 430, 825, 848, 867, 892] [365, 368, 411, 431, 826, 849, 868, 893] [366, 369, 412, 432, 827, 850, 869, 894] [367, 370, 413, 433, 828, 851, 870, 895] [368, 371, 414, 434, 829, 852, 871, 896] [369, 372, 415, 435, 830, 853, 872, 897] [370, 373, 416, 436, 831, 854, 873, 898] [374, 377, 420, 440, 835, 858, 877, 902] [375, 378, 421, 441, 836, 859, 878, 903] [376, 379, 422, 442, 837, 860, 879, 904] [377, 380, 423, 443, 838, 861, 880, 905] [378, 381, 424, 444, 839, 862, 881, 906] [379, 382, 425, 445, 840, 863, 882, 907] [380, 383, 426, 446, 841, 864, 883, 908] [381, 384, 427, 447, 842, 865, 884, 909] [382, 385, 428, 448, 843, 866, 885, 910] [383, 386, 429, 449, 844, 867, 886, 911] [384, 387, 430, 450, 845, 868, 887, 912] [385, 388, 431, 451, 846, 869, 888, 913] [386, 389, 432, 452, 847, 870, 889, 914] [387, 390, 433, 453, 848, 871, 890, 915] [388, 391, 434, 454, 849, 872, 891, 916] [389, 392, 435, 455, 850, 873, 892, 917] [390, 393, 436, 456, 851, 874, 893, 918] [391, 394, 437, 457, 852, 875, 894, 919] [392, 395, 438, 458, 853, 876, 895, 920] [0, 465] [1, 466] [2, 467] [3, 468] [4, 469] [5, 470] [6, 471] [7, 472] [8, 473] [9, 474] [10, 475] [11, 476] [12, 477] [13, 478] [14, 479] [15, 480] [16, 481] [17, 482] [2, 22, 462, 485] [3, 23, 463, 486] [4, 24, 464, 487] [6, 26, 466, 489] [7, 27, 467, 490] [8, 28, 468, 491] [9, 29, 469, 492] [10, 30, 470, 493] [11, 31, 471, 494] [12, 32, 472, 495] [13, 33, 473, 496] [14, 34, 474, 497] [15, 35, 475, 498] [16, 36, 476, 499] [17, 37, 477, 500] [18, 38, 478, 501] [19, 39, 479, 502] [20, 40, 480, 503] [3, 46, 66, 464, 465, 485, 504, 529] [4, 47, 67, 465, 466, 486, 505, 530] [5, 48, 68, 466, 467, 487, 506, 531] [6, 49, 69, 467, 468, 488, 507, 532] [7, 50, 70, 468, 469, 489, 508, 533] [8, 51, 71, 469, 470, 490, 509, 534] [9, 52, 72, 470, 471, 491, 510, 535] [10, 53, 73, 471, 472, 492, 511, 536] [11, 54, 74, 472, 473, 493, 512, 537] [12, 55, 75, 473, 474, 494, 513, 538] [13, 56, 76, 474, 475, 495, 514, 539] [14, 57, 77, 475, 476, 496, 515, 540] [15, 58, 78, 476, 477, 497, 516, 541] [16, 59, 79, 477, 478, 498, 517, 542] [17, 60, 80, 478, 479, 499, 518, 543] [18, 61, 81, 479, 480, 500, 519, 544] [19, 62, 82, 480, 481, 501, 520, 545] [20, 63, 83, 481, 482, 502, 521, 546] [24, 44, 465, 483, 507] [5, 25, 465, 488] [26, 46, 467, 484, 509] [27, 47, 468, 485, 510] [28, 48, 469, 486, 511] [29, 49, 470, 487, 512] [30, 50, 471, 488, 513] [31, 51, 472, 489, 514] [32, 52, 473, 490, 515] [33, 53, 474, 491, 516] [34, 54, 475, 492, 517] [35, 55, 476, 493, 518] [36, 56, 477, 494, 519] [37, 57, 478, 495, 520] [38, 58, 479, 496, 521] [39, 59, 480, 497, 522] [40, 60, 481, 498, 523] [41, 61, 482, 499, 524] [18, 42, 62, 500, 525] [396, 399, 442, 857, 880, 899] [397, 400, 443, 858, 881, 900] [398, 401, 444, 859, 882, 901] [399, 402, 445, 860, 883, 902] [400, 403, 446, 861, 884, 903] [401, 404, 447, 862, 885, 904] [402, 405, 448, 863, 886, 905] [403, 406, 449, 864, 887, 906] [404, 407, 450, 865, 888, 907] [405, 408, 451, 866, 889, 908] [406, 409, 452, 867, 890, 909] [407, 410, 453, 868, 891, 910] [408, 411, 454, 869, 892, 911] [409, 412, 455, 870, 893, 912] [410, 413, 456, 871, 894, 913] [411, 414, 457, 872, 895, 914] [412, 415, 458, 873, 896, 915] [413, 416, 459, 874, 897, 916] [414, 417, 460, 875, 898, 917] [418, 421, 879, 902] [419, 422, 880, 903] [420, 423, 881, 904] [421, 424, 882, 905] [422, 425, 883, 906] [423, 426, 884, 907] [424, 427, 885, 908] [425, 428, 886, 909] [426, 429, 887, 910] [427, 430, 888, 911] [428, 431, 889, 912] [429, 432, 890, 913] [430, 433, 891, 914] [431, 434, 892, 915] [432, 435, 893, 916] [433, 436, 894, 917] [434, 437, 895, 918] [435, 438, 896, 919] [436, 439, 897, 920] [440, 443, 901] [441, 444, 902] [442, 445, 903] [443, 446, 904] [444, 447, 905] [445, 448, 906] [446, 449, 907] [447, 450, 908] [448, 451, 909] [449, 452, 910] [450, 453, 911] [451, 454, 912] [452, 455, 913] [453, 456, 914] [454, 457, 915] [455, 458, 916] [456, 459, 917] [457, 460, 918] [458, 461, 919]
H_Z (450 checks, sparse supports)
[0, 25, 44, 67, 465, 526, 529] [1, 26, 45, 68, 466, 484, 527, 530] [2, 27, 46, 69, 467, 485, 528, 531] [3, 28, 47, 70, 468, 486, 529, 532] [4, 29, 48, 71, 469, 487, 530, 533] [5, 30, 49, 72, 470, 488, 531, 534] [6, 31, 50, 73, 471, 489, 532, 535] [7, 32, 51, 74, 472, 490, 533, 536] [8, 33, 52, 75, 473, 491, 534, 537] [9, 34, 53, 76, 474, 492, 535, 538] [10, 35, 54, 77, 475, 493, 536, 539] [11, 36, 55, 78, 476, 494, 537, 540] [12, 37, 56, 79, 477, 495, 538, 541] [13, 38, 57, 80, 478, 496, 539, 542] [14, 39, 58, 81, 479, 497, 540, 543] [15, 40, 59, 82, 480, 498, 541, 544] [16, 41, 60, 83, 481, 499, 542, 545] [17, 42, 61, 84, 482, 500, 543, 546] [18, 43, 62, 85, 501, 544, 547] [22, 47, 66, 89, 485, 505, 548, 551] [23, 48, 67, 90, 486, 506, 549, 552] [24, 49, 68, 91, 487, 507, 550, 553] [25, 50, 69, 92, 488, 508, 551, 554] [26, 51, 70, 93, 489, 509, 552, 555] [27, 52, 71, 94, 490, 510, 553, 556] [28, 53, 72, 95, 491, 511, 554, 557] [29, 54, 73, 96, 492, 512, 555, 558] [30, 55, 74, 97, 493, 513, 556, 559] [31, 56, 75, 98, 494, 514, 557, 560] [32, 57, 76, 99, 495, 515, 558, 561] [33, 58, 77, 100, 496, 516, 559, 562] [34, 59, 78, 101, 497, 517, 560, 563] [35, 60, 79, 102, 498, 518, 561, 564] [36, 61, 80, 103, 499, 519, 562, 565] [37, 62, 81, 104, 500, 520, 563, 566] [38, 63, 82, 105, 501, 521, 564, 567] [39, 64, 83, 106, 502, 522, 565, 568] [40, 65, 84, 107, 503, 523, 566, 569] [44, 69, 88, 111, 507, 527, 570, 573] [45, 70, 89, 112, 508, 528, 571, 574] [46, 71, 90, 113, 509, 529, 572, 575] [47, 72, 91, 114, 510, 530, 573, 576] [48, 73, 92, 115, 511, 531, 574, 577] [49, 74, 93, 116, 512, 532, 575, 578] [50, 75, 94, 117, 513, 533, 576, 579] [51, 76, 95, 118, 514, 534, 577, 580] [52, 77, 96, 119, 515, 535, 578, 581] [53, 78, 97, 120, 516, 536, 579, 582] [54, 79, 98, 121, 517, 537, 580, 583] [55, 80, 99, 122, 518, 538, 581, 584] [56, 81, 100, 123, 519, 539, 582, 585] [57, 82, 101, 124, 520, 540, 583, 586] [58, 83, 102, 125, 521, 541, 584, 587] [59, 84, 103, 126, 522, 542, 585, 588] [60, 85, 104, 127, 523, 543, 586, 589] [61, 86, 105, 128, 524, 544, 587, 590] [62, 87, 106, 129, 525, 545, 588, 591] [66, 91, 110, 133, 529, 549, 592, 595] [67, 92, 111, 134, 530, 550, 593, 596] [68, 93, 112, 135, 531, 551, 594, 597] [69, 94, 113, 136, 532, 552, 595, 598] [70, 95, 114, 137, 533, 553, 596, 599] [71, 96, 115, 138, 534, 554, 597, 600] [72, 97, 116, 139, 535, 555, 598, 601] [73, 98, 117, 140, 536, 556, 599, 602] [74, 99, 118, 141, 537, 557, 600, 603] [75, 100, 119, 142, 538, 558, 601, 604] [76, 101, 120, 143, 539, 559, 602, 605] [77, 102, 121, 144, 540, 560, 603, 606] [78, 103, 122, 145, 541, 561, 604, 607] [79, 104, 123, 146, 542, 562, 605, 608] [80, 105, 124, 147, 543, 563, 606, 609] [81, 106, 125, 148, 544, 564, 607, 610] [82, 107, 126, 149, 545, 565, 608, 611] [83, 108, 127, 150, 546, 566, 609, 612] [84, 109, 128, 151, 547, 567, 610, 613] [88, 113, 132, 155, 551, 571, 614, 617] [89, 114, 133, 156, 552, 572, 615, 618] [90, 115, 134, 157, 553, 573, 616, 619] [91, 116, 135, 158, 554, 574, 617, 620] [92, 117, 136, 159, 555, 575, 618, 621] [93, 118, 137, 160, 556, 576, 619, 622] [94, 119, 138, 161, 557, 577, 620, 623] [95, 120, 139, 162, 558, 578, 621, 624] [96, 121, 140, 163, 559, 579, 622, 625] [97, 122, 141, 164, 560, 580, 623, 626] [98, 123, 142, 165, 561, 581, 624, 627] [99, 124, 143, 166, 562, 582, 625, 628] [100, 125, 144, 167, 563, 583, 626, 629] [101, 126, 145, 168, 564, 584, 627, 630] [102, 127, 146, 169, 565, 585, 628, 631] [103, 128, 147, 170, 566, 586, 629, 632] [104, 129, 148, 171, 567, 587, 630, 633] [105, 130, 149, 172, 568, 588, 631, 634] [106, 131, 150, 173, 569, 589, 632, 635] [110, 135, 154, 177, 573, 593, 636, 639] [111, 136, 155, 178, 574, 594, 637, 640] [112, 137, 156, 179, 575, 595, 638, 641] [113, 138, 157, 180, 576, 596, 639, 642] [114, 139, 158, 181, 577, 597, 640, 643] [115, 140, 159, 182, 578, 598, 641, 644] [116, 141, 160, 183, 579, 599, 642, 645] [117, 142, 161, 184, 580, 600, 643, 646] [118, 143, 162, 185, 581, 601, 644, 647] [119, 144, 163, 186, 582, 602, 645, 648] [120, 145, 164, 187, 583, 603, 646, 649] [121, 146, 165, 188, 584, 604, 647, 650] [122, 147, 166, 189, 585, 605, 648, 651] [123, 148, 167, 190, 586, 606, 649, 652] [124, 149, 168, 191, 587, 607, 650, 653] [125, 150, 169, 192, 588, 608, 651, 654] [126, 151, 170, 193, 589, 609, 652, 655] [127, 152, 171, 194, 590, 610, 653, 656] [128, 153, 172, 195, 591, 611, 654, 657] [132, 157, 176, 199, 595, 615, 658, 661] [133, 158, 177, 200, 596, 616, 659, 662] [134, 159, 178, 201, 597, 617, 660, 663] [135, 160, 179, 202, 598, 618, 661, 664] [136, 161, 180, 203, 599, 619, 662, 665] [137, 162, 181, 204, 600, 620, 663, 666] [138, 163, 182, 205, 601, 621, 664, 667] [139, 164, 183, 206, 602, 622, 665, 668] [140, 165, 184, 207, 603, 623, 666, 669] [141, 166, 185, 208, 604, 624, 667, 670] [142, 167, 186, 209, 605, 625, 668, 671] [143, 168, 187, 210, 606, 626, 669, 672] [144, 169, 188, 211, 607, 627, 670, 673] [145, 170, 189, 212, 608, 628, 671, 674] [146, 171, 190, 213, 609, 629, 672, 675] [147, 172, 191, 214, 610, 630, 673, 676] [148, 173, 192, 215, 611, 631, 674, 677] [149, 174, 193, 216, 612, 632, 675, 678] [150, 175, 194, 217, 613, 633, 676, 679] [154, 179, 198, 221, 617, 637, 680, 683] [155, 180, 199, 222, 618, 638, 681, 684] [156, 181, 200, 223, 619, 639, 682, 685] [157, 182, 201, 224, 620, 640, 683, 686] [158, 183, 202, 225, 621, 641, 684, 687] [159, 184, 203, 226, 622, 642, 685, 688] [160, 185, 204, 227, 623, 643, 686, 689] [161, 186, 205, 228, 624, 644, 687, 690] [162, 187, 206, 229, 625, 645, 688, 691] [163, 188, 207, 230, 626, 646, 689, 692] [164, 189, 208, 231, 627, 647, 690, 693] [165, 190, 209, 232, 628, 648, 691, 694] [166, 191, 210, 233, 629, 649, 692, 695] [167, 192, 211, 234, 630, 650, 693, 696] [168, 193, 212, 235, 631, 651, 694, 697] [169, 194, 213, 236, 632, 652, 695, 698] [170, 195, 214, 237, 633, 653, 696, 699] [171, 196, 215, 238, 634, 654, 697, 700] [172, 197, 216, 239, 635, 655, 698, 701] [176, 201, 220, 243, 639, 659, 702, 705] [177, 202, 221, 244, 640, 660, 703, 706] [178, 203, 222, 245, 641, 661, 704, 707] [179, 204, 223, 246, 642, 662, 705, 708] [180, 205, 224, 247, 643, 663, 706, 709] [181, 206, 225, 248, 644, 664, 707, 710] [182, 207, 226, 249, 645, 665, 708, 711] [183, 208, 227, 250, 646, 666, 709, 712] [184, 209, 228, 251, 647, 667, 710, 713] [185, 210, 229, 252, 648, 668, 711, 714] [186, 211, 230, 253, 649, 669, 712, 715] [187, 212, 231, 254, 650, 670, 713, 716] [188, 213, 232, 255, 651, 671, 714, 717] [189, 214, 233, 256, 652, 672, 715, 718] [190, 215, 234, 257, 653, 673, 716, 719] [191, 216, 235, 258, 654, 674, 717, 720] [192, 217, 236, 259, 655, 675, 718, 721] [193, 218, 237, 260, 656, 676, 719, 722] [194, 219, 238, 261, 657, 677, 720, 723] [198, 223, 242, 265, 661, 681, 726] [199, 224, 243, 266, 662, 682, 724, 727] [200, 225, 244, 267, 663, 683, 725, 728] [201, 226, 245, 268, 664, 684, 726, 729] [202, 227, 246, 269, 665, 685, 727, 730] [203, 228, 247, 270, 666, 686, 728, 731] [204, 229, 248, 271, 667, 687, 729, 732] [205, 230, 249, 272, 668, 688, 730, 733] [206, 231, 250, 273, 669, 689, 731, 734] [207, 232, 251, 274, 670, 690, 732, 735] [208, 233, 252, 275, 671, 691, 733, 736] [209, 234, 253, 276, 672, 692, 734, 737] [210, 235, 254, 277, 673, 693, 735, 738] [211, 236, 255, 278, 674, 694, 736, 739] [212, 237, 256, 279, 675, 695, 737, 740] [213, 238, 257, 280, 676, 696, 738, 741] [214, 239, 258, 281, 677, 697, 739, 742] [215, 240, 259, 282, 678, 698, 740, 743] [216, 241, 260, 283, 679, 699, 741, 744] [220, 245, 264, 287, 683, 703, 745, 748] [221, 246, 265, 288, 684, 704, 746, 749] [222, 247, 266, 289, 685, 705, 747, 750] [223, 248, 267, 290, 686, 706, 748, 751] [224, 249, 268, 291, 687, 707, 749, 752] [225, 250, 269, 292, 688, 708, 750, 753] [226, 251, 270, 293, 689, 709, 751, 754] [227, 252, 271, 294, 690, 710, 752, 755] [228, 253, 272, 295, 691, 711, 753, 756] [229, 254, 273, 296, 692, 712, 754, 757] [230, 255, 274, 297, 693, 713, 755, 758] [231, 256, 275, 298, 694, 714, 756, 759] [232, 257, 276, 299, 695, 715, 757, 760] [233, 258, 277, 300, 696, 716, 758, 761] [234, 259, 278, 301, 697, 717, 759, 762] [235, 260, 279, 302, 698, 718, 760, 763] [236, 261, 280, 303, 699, 719, 761, 764] [237, 262, 281, 304, 700, 720, 762, 765] [238, 263, 282, 305, 701, 721, 763, 766] [242, 267, 286, 309, 705, 724, 767, 770] [243, 268, 287, 310, 706, 725, 768, 771] [244, 269, 288, 311, 707, 726, 769, 772] [245, 270, 289, 312, 708, 727, 770, 773] [246, 271, 290, 313, 709, 728, 771, 774] [247, 272, 291, 314, 710, 729, 772, 775] [248, 273, 292, 315, 711, 730, 773, 776] [249, 274, 293, 316, 712, 731, 774, 777] [250, 275, 294, 317, 713, 732, 775, 778] [251, 276, 295, 318, 714, 733, 776, 779] [252, 277, 296, 319, 715, 734, 777, 780] [253, 278, 297, 320, 716, 735, 778, 781] [254, 279, 298, 321, 717, 736, 779, 782] [255, 280, 299, 322, 718, 737, 780, 783] [256, 281, 300, 323, 719, 738, 781, 784] [257, 282, 301, 324, 720, 739, 782, 785] [258, 283, 302, 325, 721, 740, 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Code ID 921-18-31 · download JSON · raw on GitHub