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[[920,18,31]] d ≤
n
920
k
18
d
31
kd²/n
18.802
w
8
X/Z
1
g
0.058
r
4.2426
layers
2
swaps
3179

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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 witness transform · found at 2×107 trials · survived 2×107 trials · 2026-09-17
witness operator (support, 31 qubits)
[29, 41, 340, 363, 382, 407, 424, 426, 447, 449, 469, 480, 481, 495, 524, 541, 558, 587, 604, 624, 627, 630, 650, 673, 690, 716, 735, 755, 758, 801, 821]
d_Z 31 · witness weight 31 (claimed upper_bound)
witness found by @vprusso · Clifford witness transform · found at 3×108 trials · survived 3×108 trials · 2026-09-25
witness operator (support, 31 qubits)
[108, 171, 191, 211, 217, 231, 234, 251, 257, 263, 274, 280, 286, 311, 314, 317, 320, 323, 326, 329, 331, 352, 659, 684, 709, 727, 748, 750, 771, 792, 813]
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 7.06) · H_Z 2–8 (mean 7.022)
qubit degrees H_X 1–6 (mean 3.599) · H_Z 1–4 (mean 3.435)
trapping sets H_X (1,1)×64 (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): 64 (1,2): 117 (1,3): 64 (1,4): 568 (1,5): 93 (1,6): 14 (2,0): 3 (2,1): 148 (2,2): 188 (2,3): 502 (2,4): 868 (2,5): 718 (2,6): 6588 (2,7): 857 (2,8): 379 (2,9): 169 (2,10): 13 (3,0): 54 (3,1): 183 (3,2): 621 (3,3): 2304 (3,4): 3821 (3,5): 8083 (3,6): 17865 (3,7): 14228 (3,8): 107142 (3,9): 16240 (3,10): 18624 (3,11): 4794 (3,12): 2654 (3,13): 582 (3,14): 58
trapping sets H_Z (1,1)×64 (2,0)×17 (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): 64 (1,2): 131 (1,3): 66 (1,4): 659 (2,0): 17 (2,1): 139 (2,2): 280 (2,3): 460 (2,4): 940 (2,5): 738 (2,6): 7667 (3,0): 19 (3,1): 257 (3,2): 838 (3,3): 2088 (3,4): 4426 (3,5): 8283 (3,6): 20020 (3,7): 13989 (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 3179 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 @dorakingx and @DennisWayo
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Reduction of the board's codes/924-18-31.json ([[924,18,31]]) by 2 qubits at unchanged k, unchanged check-weight class and unchanged locality class, by one move applied to a fixpoint: graft a qubit away using a low-weight element of the stabilizer ROW SPACE. Let S be an element of the row space of H_X with support T and let a be in T. Replace one generator of the subset summing to S by S itself -- the span is unchanged, that generator being S plus the rest of the subset -- and add S into every other X row meeting a, so that a survives only in S. Then apply the CNOT fan-out from a to T\{a}, which acts on the check matrices as H_X[:, b] ^= H_X[:, a] and H_Z[:, a] ^= H_Z[:, b] for each b in T\{a}. Only S still meets a, so the first substitution turns S into the weight-1 stabilizer X_a and leaves every other X row alone; the second zeroes column a of H_Z, because commutation forces every Z row to meet T an even number of times. Qubit a is then disentangled and is deleted: n -> n-1, k unchanged, and the Z rows only LOSE an index, so their weights and support diameters cannot rise. The weight of S separates three regimes, and the difference is entirely in the clearing step R ^= S. |S| = 1: nothing is added anywhere, so the weights, the radius AND THE DISTANCE are all preserved exactly, and no distance search is needed -- this is the row-space form of the weight-1 stabilizer cleanup of Liang, Eberhardt and Chen (arXiv:2504.08887 Sec. III D step 4), which the implementation in research/local2d/boundary_engine.py applies only to literal weight-1 generator ROWS. |S| = 2: R loses a and toggles one other index, so its weight changes by 0 or -2 and can never rise. |S| >= 3: R can grow, so every touched row is checked against the code's weight class and its locality radius, measured in the source's own layout. This generalises the capped merge-graft I introduced with [[454,8,17]], which only ever built S from the generators a single qubit happens to lie in. Here the accepted grafts were |S| = 7: 1, |S| = 8: 1. Low-weight row-space elements are enumerated as sums of at most three checks with a connected overlap pattern. Every graft with |S| >= 2 was accepted only if k was unchanged and a bit-packed RIS search found nothing lighter than 31, screened once and confirmed twice with independent seeds; those in-loop rungs are a filter, not the evidence. QUBIT POSITIONS ARE THE SOURCE'S: every surviving qubit keeps the coordinate it has in codes/924-18-31.json, so the layout is inherited rather than re-derived, and the reduction only deletes. The surviving qubits' indices into the source numbering are [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]... (full list implied by the coordinates in this file).
model GPT-5 (Codex) (claimed, not verified)
builds on arXiv:2504.08887
date 2026-10-14
notes Recursive derivative of merged codes/922-18-31.json, not an independent construction. The merged parent was reduced by @dorakingx from codes/924-18-31.json, whose source construction is credited to @e-eight; that earlier stage used Claude Opus 5 (Claude Code). @dorakingx contributed the first additional one-qubit reduction below, producing the validated [[921,18,d<=31]] intermediate. @DennisWayo contributed the second additional reduction with GPT-5 (Codex), producing this [[920,18,d<=31]] entry. Relative to the merged [[922,18,d<=31]] parent, the two reductions preserve k=18, maximum check weight 8, bilayer locality, interaction radius 4.242640687119285, and transformed X/Z witnesses of weight 31 while deleting two physical qubits. The entry therefore improves n at the same witness-backed k and d upper bound. Two independent CI-style fire passes used seeds 2026101301 and 2027101304. Each pass ran the structural detector, the 50000-trial orbit-fold gate, 135400 ordinary RIS trials, and 8000000 RIS-fast trials. Neither pass found a logical below weight 31; RIS-fast reached weight 32 in both passes. Total post-reduction RIS search was 16270800 trials. Distance remains an upper bound, not an exact claim, and literature novelty is unverified. First additional reduction, credited to @dorakingx: X-type row-space stabilizer support [18, 483], source rows [359], removed source qubit 483, giving the [[921,18,d<=31]] intermediate. Second additional reduction, credited to @DennisWayo: X-type row-space stabilizer support [0, 465], source rows [341], removed source qubit 0, giving this [[920,18,d<=31]] entry.
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

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

X-checks 469 (max weight 8) · Z-checks 450 (max weight 8)
H_X (469 checks, sparse supports)
[2, 45, 65, 463, 464, 484, 503, 528] [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] [21, 24, 67, 87, 483, 506, 525, 550] [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] [43, 46, 89, 109, 505, 528, 547, 572] [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] [65, 68, 111, 131, 527, 550, 569, 594] [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] [87, 90, 133, 153, 549, 572, 591, 616] [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] [109, 112, 155, 175, 571, 594, 613, 638] [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] [131, 134, 177, 197, 593, 616, 635, 660] [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] [153, 156, 199, 219, 615, 638, 657, 682] [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] [175, 178, 221, 241, 637, 660, 679, 704] [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] [197, 200, 243, 263, 659, 682, 701, 725] [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] [220, 223, 266, 286, 682, 705, 723, 748] [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] [241, 244, 287, 307, 703, 725, 744, 769] [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] [263, 266, 309, 329, 724, 747, 766, 791] [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] [285, 288, 331, 351, 746, 769, 788, 813] [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] [307, 310, 353, 373, 768, 791, 810, 835] [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] [329, 332, 375, 395, 790, 813, 832, 857] [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] [351, 354, 397, 417, 812, 835, 854, 879] [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] [373, 376, 419, 439, 834, 857, 876, 901] [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] [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] [1, 21, 461, 484] [2, 22, 462, 485] [3, 23, 463, 486] [5, 25, 465, 488] [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] [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] [23, 43, 464, 482, 506] [4, 24, 464, 487] [25, 45, 466, 483, 508] [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] [17, 41, 61, 499, 524] [395, 398, 441, 856, 879, 898] [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] [417, 420, 878, 901] [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] [439, 442, 900] [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]
H_Z (450 checks, sparse supports)
[24, 43, 66, 464, 525, 528] [0, 25, 44, 67, 465, 483, 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, 500, 543, 546] [21, 46, 65, 88, 484, 504, 547, 550] [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] [43, 68, 87, 110, 506, 526, 569, 572] [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] [65, 90, 109, 132, 528, 548, 591, 594] [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] [87, 112, 131, 154, 550, 570, 613, 616] [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] [109, 134, 153, 176, 572, 592, 635, 638] [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] [131, 156, 175, 198, 594, 614, 657, 660] [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] [153, 178, 197, 220, 616, 636, 679, 682] [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] [175, 200, 219, 242, 638, 658, 701, 704] [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] [197, 222, 241, 264, 660, 680, 725] [198, 223, 242, 265, 661, 681, 723, 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] [219, 244, 263, 286, 682, 702, 744, 747] [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] [241, 266, 285, 308, 704, 723, 766, 769] [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, 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Code ID 920-18-31 · download JSON · raw on GitHub