[[721,18,24]] · QEC Challenge

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[[721,18,24]] d ≤

721

kd²/n

14.38

X/Z

1.38

0.0444

4.2426

layers

swaps

2442

Share this result

Distance

X/Z asymmetry 1.38 · d_X ≤ 33, d_Z ≤ 24 · 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 33 · witness weight 33 (claimed upper_bound)

witness found by @MathysRennela · research/kit/surrogate.lightest_logical · found at 1200 trials · survived 1200 trials · 2026-10-16

witness operator (support, 33 qubits)

[28, 31, 126, 144, 162, 164, 179, 293, 296, 316, 331, 334, 336, 351, 355, 369, 392, 406, 429, 446, 448, 463, 466, 505, 520, 541, 542, 561, 581, 598, 618, 691, 693]

d_Z 24 · witness weight 24 (claimed upper_bound)

witness found by @MathysRennela · research/kit/surrogate.distance_rand_witness (gf2_fast backend) · found at 1.5×10⁶ trials · survived 1.5×10⁶ trials · 2026-10-16

witness operator (support, 24 qubits)

[37, 91, 108, 125, 131, 142, 145, 159, 165, 179, 185, 213, 216, 219, 222, 225, 495, 517, 533, 553, 571, 589, 607, 608]

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 6.946) · H_Z 3–8 (mean 6.906)

qubit degrees H_X 1–6 (mean 3.545) · H_Z 1–4 (mean 3.362)

trapping sets H_X (1,1)×54 (2,1)×132 (3,0)×48 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_X

(1,1): 54 (1,2): 106 (1,3): 60 (1,4): 408 (1,5): 80 (1,6): 13 (2,1): 132 (2,2): 163 (2,3): 431 (2,4): 786 (2,5): 610 (2,6): 4611 (2,7): 702 (2,8): 326 (2,9): 147 (2,10): 12 (3,0): 48 (3,1): 160 (3,2): 508 (3,3): 1995 (3,4): 3317 (3,5): 6819 (3,6): 15147 (3,7): 12098 (3,8): 72682 (3,9): 13024 (3,10): 13789 (3,11): 3945 (3,12): 2237 (3,13): 503 (3,14): 51

trapping sets H_Z (1,1)×59 (2,0)×18 (3,0)×15 (smallest syndrome weight at each size, connected sets of up to 3 qubits)

full (size, syndrome weight): count census for H_Z

(1,1): 59 (1,2): 113 (1,3): 57 (1,4): 492 (2,0): 18 (2,1): 124 (2,2): 238 (2,3): 403 (2,4): 803 (2,5): 633 (2,6): 5545 (3,0): 15 (3,1): 221 (3,2): 725 (3,3): 1798 (3,4): 3793 (3,5): 7099 (3,6): 16349 (3,7): 11864 (3,8): 88979 (3,9): 1050 (3,10): 9857

witness diameter X 18.6815 · Z 21.6333 (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

X checkZ checkqubit site (361)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 2442 nearest-neighbor SWAPs per round in total, at most 4 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 @MathysRennela

provenance submitted through the challenge

novelty novelty not audited

construction r=1 graft reduction of 722-18-25 by 1 qubits at unchanged k=18, unchanged check-weight class and unchanged locality class, via research/local2d/boundary_engine.graft_r1_safe(d_floor=24); each removal keeps k and is confirmed at two fresh seeds. Bilayer layout inherited from the parent with the removed coordinates dropped.

model MiMo-V2.6-Flash (OpenCode agent harness) (claimed, not verified)

builds on arXiv:2504.08887, arXiv:2504.09171

date 2026-10-16

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

[[721,18,24]] — r=1 graft reduction of the 19x19 tile code (weight-8, bilayer)

Direction & hypothesis

Cell weight-8 / local-2d-bilayer, family tile. Once the k=18 tile ladder was filled ([[612,18,21]], [[648,18,23]], [[722,18,24]] — see their notes), the remaining opening in this family was a **smaller-n point at the same rung**: anything with n < 722 at d >= 24 strictly dominates [[722,18,24]] and sits on the frontier ahead of it. Building bigger lattices cannot do that (19x21 and above only raise n), so this entry comes from **removing qubits at unchanged k and distance** — the r=1 graft move of arXiv:2504.08887 Sec. III E, which the board's other shrunk tile entries (e.g. [[474,18,18]] from [[512,18,18]]) were built with.

What was searched

Parent: the confirmed [[722,18,24]] (a 19x19 lattice, `build_planar(19, 19, S_F_TILE4, S_G_TILE4_MAIN)`). The chain calls research/local2d/boundary_engine.graft_r1_safe with an **explicit d_floor=24** taken from the parent's own 1.5M-trial confirmation — never from a cheap baseline, since an under-converged floor silently licenses distance-losing removals.

Per removal the tool screens at 400 NumPy RIS trials (seed 1) and keeps a removal only after two fresh-seed confirmations at 900 trials; after each accepted removal the campaign's driver (not committed; the recipe below reproduces it) re-measures the code at 200,000 gf2_fast trials and runs the verifier's own _stabilizer_block_count, because the gate rejects a disconnected stabilizer group outright. Qubit identity is tracked through the removals so the parent's bilayer layout survives (the removed qubit's coordinate is dropped, which is how the board's other graft-derived tile entries keep their locality class).

Chain, with the seed schedule it is reproducible under (seed=1000+step):

step 1: removed qubit 347 -> n=721, connected, 200k-trial reading d <= 25
step 2: removed qubit 372 -> n=720, splits into 2 blocks (sizes [719, 1])

-> chain stopped; the gate would have refused it

Evidence trail

200,000 fast trials (per-step): d <= 25
1,500,000 fast trials, fresh seed: d <= 24 (Z-side witness of weight 24)

So the 25 was soft — the same drift the parent showed (packaged 26, confirmed 25, submission search 24), and the reason this entry claims 24.

The reverse also happened and is worth recording: a later 2,000,000-trial search on a different seed missed the weight-24 logical and read d <= 25 (X side). The claim here is 24 because the weight-24 operator is in the file and the verifier re-checks it — the deeper search's miss does not make the exhibited logical heavier. This entry is therefore filed by hand rather than through ./qldpc submit, which would have taken its own search's weaker number. The claim is a witness-backed upper bound, not exact: k=18 is far outside verify/certify.py's envelope (certified codes today: d <= 13, k <= 12), and the board's weekly 3e8-trial sweep remains the final refuter.

On the frontier: the gate reports board_advancing: true, dominated_by: [], and this entry strictly dominates [[722,18,24]] on n at equal k, d and w.

Dead ends

The graft cannot go below n=721 on this parent: the next removal (qubit

372) orphans a single qubit, and _stabilizer_block_count reports 2 blocks. A 6-removal chain reached n=716 with per-step readings 25/25/26/25/24/25 and was refused by the gate for the same reason (stabilizer_group_connected). The reductions are therefore real but shallow: one qubit, not the 6-38 the board's other graft entries took.

Per-step readings of 25 and even 26 at 200k trials were all soft: at 1.5M

every intermediate lands at 24. This is the third time in this campaign that a shallower budget read a lighter logical as heavier, which is why every claim here carries its budget in witness_provenance.

[[760,18,25]] (a 19x20 lattice, confirmed at 1.5M and 2M) still holds rung

25 at larger n; it is staged but unsubmitted, since this entry does not displace it and one code per PR is the rule.

Tools

Model: MiMo-V2.6-Flash, driven as an OpenCode agent harness; repository tooling only: research/local2d/boundary_engine.py (graft_r1_safe), research/kit/surrogate.py with the gf2_fast accelerator (make fast), verify/qldpc_verify.py's connectivity test, research/kit/submit.py, research/kit/coordination.py. Roughly 2 CPU core-hours for the chain plus the 1.5M-trial confirmation.

Reproduction

import sys; sys.path[:0] = ["research/kit", "research/local2d", "verify"]
from boundary_engine import build_planar, graft_r1_safe, S_F_TILE4, S_G_TILE4_MAIN
HX, HZ, info = build_planar(19, 19, S_F_TILE4, S_G_TILE4_MAIN)   # [[722,18,24]]
HX, HZ, removed = graft_r1_safe(HX, HZ, max_removals=1, trials=400,
                                confirm_trials=900, seed=1000, d_floor=24)
# removed == 1; the dropped qubit is original index 347, so the layout is the
# parent's grid_coordinates(19, 19) with that coordinate deleted

The campaign driver runs exactly this chain — the connectivity check (_stabilizer_block_count, verify/qldpc_verify.py) and the 1.5M-trial confirmation included — and records every intermediate in its own manifest.

Parity checks

X-checks 368 (max weight 8) · Z-checks 351 (max weight 8)

H_X (368 checks, sparse supports)

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

H_Z (351 checks, sparse supports)

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

Code ID 721-18-24 · download JSON · raw on GitHub