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[[792,18,27]] d ≤
n
792
k
18
d
27
kd²/n
16.568
w
8
X/Z
1.04
g
0.0082
r
6.7082
layers
2
swaps
2708

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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 witness transform · found at 3×108 trials · survived 1.6×107 trials · 2026-10-09
witness operator (support, 28 qubits)
[6, 9, 13, 36, 289, 310, 327, 350, 365, 367, 386, 388, 450, 465, 492, 507, 525, 528, 531, 549, 570, 585, 608, 626, 644, 647, 686, 704]
d_Z 27 · witness weight 27 (claimed upper_bound)
witness found by @dorakingx · Clifford witness transform · found at 5×106 trials · survived 1.6×107 trials · 2026-10-04
witness operator (support, 27 qubits)
[6, 9, 13, 23, 24, 31, 34, 42, 54, 77, 80, 99, 407, 410, 418, 423, 427, 429, 432, 449, 452, 457, 459, 474, 476, 478, 497]
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 7.063) · H_Z 2–8 (mean 6.926)
qubit degrees H_X 1–8 (mean 3.532) · H_Z 1–4 (mean 3.419)
trapping sets H_X (1,1)×61 (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): 61 (1,2): 110 (1,3): 66 (1,4): 472 (1,5): 71 (1,6): 10 (1,7): 1 (1,8): 1 (2,0): 4 (2,1): 138 (2,2): 185 (2,3): 482 (2,4): 813 (2,5): 722 (2,6): 5321 (2,7): 731 (2,8): 272 (2,9): 121 (2,10): 23 (2,11): 10 (2,12): 2 (3,0): 51 (3,1): 174 (3,2): 602 (3,3): 2197 (3,4): 3695 (3,5): 7748 (3,6): 16203 (3,7): 14162 (3,8): 85013 (3,9): 13721 (3,10): 14500 (3,11): 3807 (3,12): 2015 (3,13): 543 (3,14): 185 (3,15): 57 (3,16): 7
trapping sets H_Z (1,1)×54 (2,0)×13 (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): 54 (1,2): 119 (1,3): 60 (1,4): 559 (2,0): 13 (2,1): 119 (2,2): 249 (2,3): 407 (2,4): 848 (2,5): 666 (2,6): 6395 (3,0): 16 (3,1): 216 (3,2): 722 (3,3): 1817 (3,4): 3911 (3,5): 7311 (3,6): 17626 (3,7): 12530 (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 2708 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. Derived by a one-qubit Clifford reduction on X-type row-space stabilizer support [0, 399], removing source qubit 0. The row-space element used source rows [285]. Distance remains a witness-backed upper bound.
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 396 (max weight 8) · Z-checks 391 (max weight 8)
H_X (396 checks, sparse supports)
[0, 3, 41, 59, 399, 419, 435, 458] [1, 42, 60, 400, 404, 420, 436, 459] [2, 4, 43, 61, 401, 421, 437, 460] [3, 5, 44, 62, 402, 422, 438, 461] [6, 45, 63, 403, 404, 423, 439, 462] [4, 7, 46, 64, 404, 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] [17, 20, 59, 77, 416, 436, 453, 476] [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] [37, 40, 79, 97, 435, 456, 473, 496] [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] [57, 60, 99, 117, 455, 476, 493, 516] [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] [77, 80, 119, 137, 475, 496, 513, 536] [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] [97, 100, 139, 157, 495, 516, 533, 556] [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] [117, 120, 159, 177, 515, 536, 553, 576] [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] [137, 140, 179, 197, 535, 556, 573, 595] [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] [157, 160, 199, 217, 555, 576, 593, 615] [159, 162, 201, 219, 557, 578, 594, 617] [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] [177, 180, 219, 237, 575, 595, 612, 635] [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] [197, 200, 239, 257, 594, 615, 632, 655] [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] [217, 220, 259, 277, 614, 635, 652, 675] [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] [237, 240, 279, 297, 634, 655, 672, 695] [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] [257, 260, 299, 317, 654, 675, 692, 715] [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] [277, 280, 319, 337, 674, 695, 712, 735] [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] [297, 300, 339, 357, 694, 715, 732, 755] [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] [317, 320, 359, 377, 714, 735, 752, 775] [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] [2, 40, 58, 398, 399, 418, 434, 457] [0, 400] [1, 401] [2, 402] [3, 403] [4, 405] [5, 406] [6, 407] [7, 408] [8, 409] [9, 410] [10, 411] [11, 412] [12, 413] [0, 17, 396, 417] [2, 19, 397, 419] [3, 20, 398, 420] [21, 399, 404, 421] [4, 22, 400, 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] [3, 41, 59, 399, 400, 419, 435, 458] [42, 60, 400, 401, 404, 420, 436, 459] [4, 43, 61, 401, 402, 421, 437, 460] [5, 44, 62, 402, 403, 422, 438, 461] [7, 46, 64, 404, 405, 424, 440, 463] [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] [12, 13, 16, 55, 73, 433, 449, 472] [19, 37, 398, 414, 436] [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] [12, 13, 35, 53, 413, 430, 452] [337, 340, 379, 734, 755, 772] [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] [352, 355, 394, 749, 770, 787] [353, 356, 395, 750, 771, 788] [357, 360, 754, 775] [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] [377, 380, 774] [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] [351, 354, 372, 375, 393, 748, 786, 790]
H_Z (391 checks, sparse supports)
[20, 37, 58, 398, 415, 453, 456] [21, 38, 59, 399, 416, 454, 457] [0, 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] [26, 43, 64, 404, 421, 459, 462] [4, 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, 431, 469, 472] [17, 40, 57, 78, 417, 434, 473, 476] [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] [37, 60, 77, 98, 436, 454, 493, 496] [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] [57, 80, 97, 118, 456, 474, 513, 516] [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] [77, 100, 117, 138, 476, 494, 533, 536] [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] [97, 120, 137, 158, 496, 514, 553, 556] [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] [117, 140, 157, 178, 516, 534, 573, 576] [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] [137, 160, 177, 198, 536, 554, 593, 595] [138, 161, 178, 199, 537, 555, 596] [139, 162, 179, 200, 538, 556, 594, 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] [157, 180, 197, 218, 556, 574, 612, 615] [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] [177, 200, 217, 238, 576, 632, 635] [178, 201, 218, 239, 577, 594, 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] [197, 220, 237, 258, 595, 613, 652, 655] [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] [217, 240, 257, 278, 615, 633, 672, 675] [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] [237, 260, 277, 298, 635, 653, 692, 695] [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] [257, 280, 297, 318, 655, 673, 712, 715] [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] [277, 300, 317, 338, 675, 693, 732, 735] [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] [297, 320, 337, 358, 695, 713, 752, 755] [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] [317, 340, 357, 378, 715, 733, 772, 775] [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] [17, 396, 453] [37, 414, 473] [57, 493] [77, 453, 513] [97, 473, 533] [117, 493, 553] [137, 513, 573] [157, 533, 593] [177, 553, 612] [197, 573, 632] [217, 593, 652] [237, 612, 672] [257, 632, 692] [277, 652, 712] [297, 672, 732] [317, 692, 752] [337, 712, 772] [18, 454] [38, 415, 474] [58, 434, 494] [78, 454, 514] [98, 474, 534] [118, 494, 554] [138, 514, 574] [158, 534] [178, 554, 613] [198, 574, 633] [218, 653] [238, 613, 673] [258, 633, 693] [278, 653, 713] [298, 673, 733] [318, 693, 753] [338, 713, 773] [19, 57, 397, 414, 455] [39, 77, 416, 475] [59, 97, 435, 453, 495] [79, 117, 455, 473, 515] [99, 137, 475, 493, 535] [119, 157, 495, 513, 555] [139, 177, 515, 533, 575] [159, 197, 535, 553, 594] [179, 217, 555, 573, 614] [199, 237, 575, 593, 634] [219, 257, 594, 612, 654] [239, 277, 614, 632, 674] [259, 297, 634, 652, 694] [279, 317, 654, 672, 714] [299, 337, 674, 692, 734] [319, 357, 694, 712, 754] [339, 377, 714, 732, 774] [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, 751, 790] [14, 54, 75, 432, 470] [34, 74, 95, 451, 490] [54, 94, 115, 471, 510] [74, 114, 135, 491, 530] [94, 134, 155, 511, 550] [114, 154, 175, 531, 570] [134, 174, 195, 551, 590] [154, 194, 215, 571, 609] [174, 214, 235, 591, 629] [194, 234, 255, 610, 649] [214, 254, 275, 630, 669] [234, 274, 295, 650, 689] [254, 294, 315, 670, 709] [274, 314, 335, 690, 729] [294, 334, 355, 710, 749] [314, 354, 375, 730, 769] [334, 374, 395, 750, 789] [16, 56, 472] [36, 76, 492] [56, 96, 512] [76, 116, 532] [96, 136, 552] [116, 156, 572] [136, 176, 592] [156, 196, 611] [176, 216, 631] [196, 236, 651] [216, 256, 671] [236, 276, 691] [256, 296, 711] [276, 316, 731] [296, 336, 751] [316, 356, 771] [336, 376, 791]
Code ID 792-18-27 · download JSON · raw on GitHub