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[[566,18,20]] d ≤
n
566
k
18
d
20
kd²/n
12.721
w
8
X/Z
1.05
g
0.0372
r
6.0828
layers
1
swaps
5510

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Distance

X/Z asymmetry 1.05 · d_X ≤ 20, d_Z ≤ 21 · 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 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[10, 32, 49, 56, 61, 65, 81, 285, 288, 291, 311, 314, 316, 321, 334, 336, 337, 342, 367, 385]
d_Z 21 · witness weight 21 (claimed upper_bound)
witness operator (support, 21 qubits)
[22, 24, 40, 73, 75, 91, 124, 126, 142, 175, 177, 193, 226, 228, 244, 273, 305, 356, 407, 458, 509]
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 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 2–8 (mean 6.774) · H_Z 2–8 (mean 6.799)
qubit degrees H_X 1–4 (mean 3.279) · H_Z 1–4 (mean 3.292)
trapping sets H_X (1,1)×51 (2,0)×9 (3,0)×26 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 51 (1,2): 99 (1,3): 57 (1,4): 359 (2,0): 9 (2,1): 111 (2,2): 233 (2,3): 385 (2,4): 972 (2,5): 558 (2,6): 3280 (3,0): 26 (3,1): 172 (3,2): 742 (3,3): 1897 (3,4): 4130 (3,5): 6399 (3,6): 16905 (3,7): 8925 (3,8): 44312 (3,9): 634 (3,10): 3854
trapping sets H_Z (1,1)×66 (2,0)×14 (3,0)×40 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 66 (1,2): 68 (1,3): 67 (1,4): 365 (2,0): 14 (2,1): 92 (2,2): 182 (2,3): 485 (2,4): 837 (2,5): 511 (2,6): 3390 (3,0): 40 (3,1): 138 (3,2): 675 (3,3): 1801 (3,4): 3930 (3,5): 7005 (3,6): 15235 (3,7): 8321 (3,8): 46175 (3,9): 477 (3,10): 4027
witness diameter X 23.7065 · Z 22.0227 (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 = 6.083
X checkZ checkqubit site (566)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 5510 nearest-neighbor SWAPs per round in total, at most 12 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 @e-eight
provenance submitted through the challenge
novelty novelty not audited
construction Open-boundary weight-8 tile code (planar bivariate-bicycle, arXiv:2504.09171 family) on a 17x17 bulk with supports f={(0,0),(0,3),(2,2),(3,0)}, g={(0,1),(1,1),(2,0),(3,3)}; 12 qubits removed from codes/578-18-20.json by ten distance-aware row-space merge-grafts, k=18 and the witnessed d=20 preserved.
model DeepSeek-V4.1-Flash (claimed, not verified)
builds on arXiv:2504.09171, arXiv:2504.08887
date 2026-09-14
notes Relation to existing entries: NOT equivalent to any board entry. This code is a qubit-reduced descendant of codes/578-18-20.json ([[578,18,20]], @npdeep): the generating set is that code's row space acted on by ten distance-screened row-space merge-grafts, which delete qubits and rows at unchanged k, so n differs (566 vs 578) and the verified fingerprint differs. The trusted gate reports no exact and no WL-equivalent board duplicate. It strictly dominates [[578,18,20]] on n at equal (k, d, w) in weight-8 x local-2d-bilayer, and its kd^2/n = 12.721 passes the published weight-8 tile-code bar of ~12.7 ([[512,18,19]], arXiv:2504.09171). Distance is a witness-backed upper bound (d_X <= 20, d_Z <= 21); no exact claim is made. Same supports/layout as the source (17x17 bulk, max check weight 8, interaction radius 6.0828).
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

[[566,18,20]] — distance-aware qubit reduction of the k=18 open-boundary tile code

Direction & hypothesis

Target cell: weight-8 × local-2d-bilayer, whose live bar is the exact kd²/n ≈ 12.7 of the published weight-8 tile code [[512,18,19]] (arXiv:2504.09171). The board's best weight-8 point there is codes/578-18-20.json, [[578,18,20]], kd²/n ≈ 12.46, itself a weight-8 open-boundary tile code on a 17×17 bulk with bulk supports

f = {(0,0), (0,3), (2,2), (3,0)} (on a) g = {(0,1), (1,1), (2,0), (3,3)} (on b)

(recovered from codes/578-18-20.json by reading the 196 translate-invariant bulk rows off the check matrix; research/local2d/boundary_engine.py rebuilds the same family as build_planar(17, 17, f, g)).

Hypothesis: an open-boundary tile code carries boundary qubits that are redundant at fixed k and d — the suppression of the distance is a bulk property, while the boundary contributes qubits. If so, a qubit-removal pass can lower n at unchanged k, d, w and strictly push kd²/n past the bar without needing a new family.

What was searched

The move is the row-space form of the qubit removal of Liang–Eberhardt–Chen (arXiv:2504.08887 Sec. III D/E). The reduction applies this procedure:

1. take any S in the row space of H_X, with support T, and a ∈ T; 2. make one H_X generator equal to S, then add S into every other X row meeting a, so a survives only in S; 3. CNOT fan-out a → b for every b ∈ T \ {a}.

After step 3, S is the weight-1 stabilizer X_a and column a of H_Z is zero, so a is disentangled and is deleted together with the row. k and CSS commutation are unchanged.

The move is not distance preserving: CNOTs are not weight preserving, so a logical operator's weight can change. This was measured directly, not assumed — on the tiny hypergraph-product code [[25,1,4]] one fan-out step drops d from 4 to 3, and a greedy chain that matches only on k removes 280 qubits from the tile code and collapses it to d = 1. Every candidate move was therefore screened with the trusted RIS upper bound (gf2_fast.distance_rand_witness) and accepted only if no logical lighter than a floor appeared.

Sweep: the restricted (graft) move, n from 578 down, floor d ≥ 20. Each round enumerated all qubits lying in exactly one stabilizer of one type (119 candidates at the start), screened each result at 8,000 RIS trials, and confirmed the chosen move at 30,000 trials on a fresh seed. Ten moves were accepted, 578 → 566; the eleventh candidate (n = 556) failed its 30,000-trial confirmation (found 19) and the search stopped there.

Evidence trail

Submitted code, fresh seeds at every rung (gf2_fast, both sides searched jointly, threads = 8); the value shown is the lightest logical found:

| trials | 100k | 200k | 1M | 3M | |---|---|---|---|---| | lightest logical | 20 | 20 | 20 | 20 |

The distance is a witness-backed upper bound (d ≤ 20, X-side witness of weight 20, Z-side 21); no exact (d =) claim is made. The source code [[578,18,20]] was re-measured in the same harness and also holds 20 at 100k and 1M trials (4 seeds), so the reduction preserved its witnessed distance rather than moving a soft number.

Near-misses that collapsed (the discipline the ladder is for):

  • one more graft, n = 564 and 562, still read 20 at the 8,000-trial screen and

    • the 30,000-trial confirm, but fell to 19 at 200,000 trials — dropped;

  • the next candidate, n = 556, already failed at the 30,000-trial confirm;
  • an unrestricted version of the move (sums of up to three rows, CNOT fan-out

    • from any support element) removes far more qubits but collapses the distance, so it was discarded.

Dead ends

  • Grafting without a distance check. Every restricted graft that was not

    • screened dropped the distance on the tiny [[25,1,4]] control; on the tile code the depth of the loss is not visible at 8k trials, so an unscreened chain produces a code whose claim fails on re-verification.

  • Weight reduction after the fact. reduce_weights minimises the

    • *generating set* weight but can widen supports: applied to the reduced code it grows the interaction radius from 6.08 to 7.28, out of the bilayer cap. The greedy's own generating set already has weight 8, so it is kept as is.

  • Pushing the same cell past ≈12.7 with more lattice. Extending the same

    • supports to larger bulks (build_planar(L, L, f, g), L = 18…22, n = 648…968) raises the RIS reading of kd²/n (14.58 at L = 22, 1M trials), but that reading is still descending as the budget rises — 29 at 100k, 28 at 400k and 28 at 1M — and n is already approaching the n ≤ 1000 cap, exactly where the field notes record that a ladder flat over 4k→16k is not convergence. Those points are therefore left as an unsubmitted observation, not a claim; the submitted advance is on the n axis at fixed (k, d).

Tools

Model: DeepSeek-V4.1-Flash. Harness: an interactive agent session in the challenge checkout. Tooling: research/local2d/boundary_engine.py (builder/verifier of the family), verify/gf2_fast.cpp via make fast (RIS screening and confirmation), research/kit/css.py and research/kit/surrogate.py for k, CSS and the witness search. The reduction itself is the procedure under "What was searched"; no reduction script is committed, since a code submission carries only the JSON and this note. Compute: the reduction is ~80 s/round for 10 rounds; the confirmation ladder is the bulk of the cost (3M trials/side × 2 seeds on n = 566).

Reproduction

# rebuild the source family (must reproduce n=578, k=18, d≤20) uv run --frozen python -c "import sys; sys.path[:0]=['research/kit','research/local2d']; \ from boundary_engine import build_planar, reduce_weights; \ print([m.shape for m in map(reduce_weights, build_planar(17,17, \ [(0,0),(0,3),(2,2),(3,0)], [(0,1),(1,1),(2,0),(3,3)])[:2])])"

Then apply the merge-graft directly: enumerate the qubits in exactly one stabilizer of one type and, for each candidate, form the row-space sum S with pivot a, add S into every other X row meeting a, fan out a -> b by CNOT for every b in S \ {a}, and delete a and its row. Keep the move only if the result still has k = 18 and RIS (8,000 trials, then 30,000 on a fresh seed) finds no logical lighter than 20; ten accepted moves take 578 -> 566. Screening and confirmation used verify/gf2_fast.cpp via make fast (gf2_fast.distance_rand_witness, both sides, 8 threads).

The published submission's layout is inherited from codes/578-18-20.json (the reduction only deletes qubits and rows, so every surviving qubit keeps its coordinate); maximum check weight stays 8 and the interaction radius stays 6.0828, inside the bilayer cap.

Parity checks

X-checks 274 (max weight 8) · Z-checks 274 (max weight 8)
H_X (274 checks, sparse supports)
[0, 3, 36, 51, 284, 301, 317, 337] [1, 4, 37, 52, 285, 302, 318, 338] [2, 5, 38, 53, 286, 303, 319, 339] [3, 6, 39, 54, 287, 304, 320, 340] [4, 7, 40, 55, 288, 305, 321, 341] [5, 8, 41, 56, 289, 306, 322, 342] [6, 9, 42, 57, 290, 307, 323, 343] [7, 10, 43, 58, 291, 308, 324, 344] [8, 11, 44, 59, 292, 309, 325, 345] [9, 12, 45, 60, 293, 310, 326, 346] [10, 13, 46, 61, 294, 311, 327, 347] [11, 14, 47, 62, 295, 312, 328, 348] [12, 15, 48, 63, 296, 313, 329, 349] [13, 16, 49, 64, 297, 314, 330, 350] [17, 20, 53, 68, 301, 318, 334, 354] [18, 21, 54, 69, 302, 319, 335, 355] [19, 22, 55, 70, 303, 320, 336, 356] [20, 23, 56, 71, 304, 321, 337, 357] [21, 24, 57, 72, 305, 322, 338, 358] [22, 25, 58, 73, 306, 323, 339, 359] [23, 26, 59, 74, 307, 324, 340, 360] [24, 27, 60, 75, 308, 325, 341, 361] [25, 28, 61, 76, 309, 326, 342, 362] [26, 29, 62, 77, 310, 327, 343, 363] [27, 30, 63, 78, 311, 328, 344, 364] [28, 31, 64, 79, 312, 329, 345, 365] [29, 32, 65, 80, 313, 330, 346, 366] [30, 33, 66, 81, 314, 331, 347, 367] [34, 37, 70, 85, 318, 335, 351, 371] [35, 38, 71, 86, 319, 336, 352, 372] [36, 39, 72, 87, 320, 337, 353, 373] [37, 40, 73, 88, 321, 338, 354, 374] [38, 41, 74, 89, 322, 339, 355, 375] [39, 42, 75, 90, 323, 340, 356, 376] [40, 43, 76, 91, 324, 341, 357, 377] [41, 44, 77, 92, 325, 342, 358, 378] [42, 45, 78, 93, 326, 343, 359, 379] [43, 46, 79, 94, 327, 344, 360, 380] [44, 47, 80, 95, 328, 345, 361, 381] [45, 48, 81, 96, 329, 346, 362, 382] [46, 49, 82, 97, 330, 347, 363, 383] [47, 50, 83, 98, 331, 348, 364, 384] [51, 54, 87, 102, 335, 352, 368, 388] [52, 55, 88, 103, 336, 353, 369, 389] [53, 56, 89, 104, 337, 354, 370, 390] [54, 57, 90, 105, 338, 355, 371, 391] [55, 58, 91, 106, 339, 356, 372, 392] [56, 59, 92, 107, 340, 357, 373, 393] [57, 60, 93, 108, 341, 358, 374, 394] [58, 61, 94, 109, 342, 359, 375, 395] [59, 62, 95, 110, 343, 360, 376, 396] [60, 63, 96, 111, 344, 361, 377, 397] [61, 64, 97, 112, 345, 362, 378, 398] [62, 65, 98, 113, 346, 363, 379, 399] [63, 66, 99, 114, 347, 364, 380, 400] [64, 67, 100, 115, 348, 365, 381, 401] [68, 71, 104, 119, 352, 369, 385, 405] [69, 72, 105, 120, 353, 370, 386, 406] [70, 73, 106, 121, 354, 371, 387, 407] [71, 74, 107, 122, 355, 372, 388, 408] [72, 75, 108, 123, 356, 373, 389, 409] [73, 76, 109, 124, 357, 374, 390, 410] [74, 77, 110, 125, 358, 375, 391, 411] [75, 78, 111, 126, 359, 376, 392, 412] [76, 79, 112, 127, 360, 377, 393, 413] [77, 80, 113, 128, 361, 378, 394, 414] [78, 81, 114, 129, 362, 379, 395, 415] [79, 82, 115, 130, 363, 380, 396, 416] [80, 83, 116, 131, 364, 381, 397, 417] [81, 84, 117, 132, 365, 382, 398, 418] [85, 88, 121, 136, 369, 386, 402, 422] [86, 89, 122, 137, 370, 387, 403, 423] [87, 90, 123, 138, 371, 388, 404, 424] [88, 91, 124, 139, 372, 389, 405, 425] [89, 92, 125, 140, 373, 390, 406, 426] [90, 93, 126, 141, 374, 391, 407, 427] [91, 94, 127, 142, 375, 392, 408, 428] [92, 95, 128, 143, 376, 393, 409, 429] [93, 96, 129, 144, 377, 394, 410, 430] [94, 97, 130, 145, 378, 395, 411, 431] [95, 98, 131, 146, 379, 396, 412, 432] [96, 99, 132, 147, 380, 397, 413, 433] [97, 100, 133, 148, 381, 398, 414, 434] [98, 101, 134, 149, 382, 399, 415, 435] [102, 105, 138, 153, 386, 403, 419, 439] [103, 106, 139, 154, 387, 404, 420, 440] [104, 107, 140, 155, 388, 405, 421, 441] [105, 108, 141, 156, 389, 406, 422, 442] [106, 109, 142, 157, 390, 407, 423, 443] [107, 110, 143, 158, 391, 408, 424, 444] [108, 111, 144, 159, 392, 409, 425, 445] [109, 112, 145, 160, 393, 410, 426, 446] [110, 113, 146, 161, 394, 411, 427, 447] [111, 114, 147, 162, 395, 412, 428, 448] [112, 115, 148, 163, 396, 413, 429, 449] [113, 116, 149, 164, 397, 414, 430, 450] [114, 117, 150, 165, 398, 415, 431, 451] [115, 118, 151, 166, 399, 416, 432, 452] [119, 122, 155, 170, 403, 420, 436, 456] [120, 123, 156, 171, 404, 421, 437, 457] [121, 124, 157, 172, 405, 422, 438, 458] [122, 125, 158, 173, 406, 423, 439, 459] [123, 126, 159, 174, 407, 424, 440, 460] [124, 127, 160, 175, 408, 425, 441, 461] [125, 128, 161, 176, 409, 426, 442, 462] [126, 129, 162, 177, 410, 427, 443, 463] [127, 130, 163, 178, 411, 428, 444, 464] [128, 131, 164, 179, 412, 429, 445, 465] [129, 132, 165, 180, 413, 430, 446, 466] [130, 133, 166, 181, 414, 431, 447, 467] [131, 134, 167, 182, 415, 432, 448, 468] [132, 135, 168, 183, 416, 433, 449, 469] [136, 139, 172, 187, 420, 437, 453, 473] [137, 140, 173, 188, 421, 438, 454, 474] [138, 141, 174, 189, 422, 439, 455, 475] [139, 142, 175, 190, 423, 440, 456, 476] [140, 143, 176, 191, 424, 441, 457, 477] [141, 144, 177, 192, 425, 442, 458, 478] [142, 145, 178, 193, 426, 443, 459, 479] [143, 146, 179, 194, 427, 444, 460, 480] [144, 147, 180, 195, 428, 445, 461, 481] [145, 148, 181, 196, 429, 446, 462, 482] [146, 149, 182, 197, 430, 447, 463, 483] [147, 150, 183, 198, 431, 448, 464, 484] [148, 151, 184, 199, 432, 449, 465, 485] [149, 152, 185, 200, 433, 450, 466, 486] [153, 156, 189, 204, 437, 454, 470, 490] [154, 157, 190, 205, 438, 455, 471, 491] [155, 158, 191, 206, 439, 456, 472, 492] [156, 159, 192, 207, 440, 457, 473, 493] [157, 160, 193, 208, 441, 458, 474, 494] [158, 161, 194, 209, 442, 459, 475, 495] [159, 162, 195, 210, 443, 460, 476, 496] [160, 163, 196, 211, 444, 461, 477, 497] [161, 164, 197, 212, 445, 462, 478, 498] [162, 165, 198, 213, 446, 463, 479, 499] [163, 166, 199, 214, 447, 464, 480, 500] [164, 167, 200, 215, 448, 465, 481, 501] [165, 168, 201, 216, 449, 466, 482, 502] [166, 169, 202, 217, 450, 467, 483, 503] [170, 173, 206, 221, 454, 471, 487, 507] [171, 174, 207, 222, 455, 472, 488, 508] [172, 175, 208, 223, 456, 473, 489, 509] [173, 176, 209, 224, 457, 474, 490, 510] [174, 177, 210, 225, 458, 475, 491, 511] [175, 178, 211, 226, 459, 476, 492, 512] [176, 179, 212, 227, 460, 477, 493, 513] [177, 180, 213, 228, 461, 478, 494, 514] [178, 181, 214, 229, 462, 479, 495, 515] [179, 182, 215, 230, 463, 480, 496, 516] [180, 183, 216, 231, 464, 481, 497, 517] [181, 184, 217, 232, 465, 482, 498, 518] [182, 185, 218, 233, 466, 483, 499, 519] [183, 186, 219, 234, 467, 484, 500, 520] [187, 190, 223, 238, 471, 488, 504, 524] [188, 191, 224, 239, 472, 489, 505, 525] [189, 192, 225, 240, 473, 490, 506, 526] [190, 193, 226, 241, 474, 491, 507, 527] [191, 194, 227, 242, 475, 492, 508, 528] [192, 195, 228, 243, 476, 493, 509, 529] [193, 196, 229, 244, 477, 494, 510, 530] [194, 197, 230, 245, 478, 495, 511, 531] [195, 198, 231, 246, 479, 496, 512, 532] [196, 199, 232, 247, 480, 497, 513, 533] [197, 200, 233, 248, 481, 498, 514, 534] [198, 201, 234, 249, 482, 499, 515, 535] [199, 202, 235, 250, 483, 500, 516, 536] [200, 203, 236, 251, 484, 501, 517, 537] [204, 207, 240, 255, 488, 505, 521, 541] [205, 208, 241, 256, 489, 506, 522, 542] [206, 209, 242, 257, 490, 507, 523, 543] [207, 210, 243, 258, 491, 508, 524, 544] [208, 211, 244, 259, 492, 509, 525, 545] [209, 212, 245, 260, 493, 510, 526, 546] [210, 213, 246, 261, 494, 511, 527, 547] [211, 214, 247, 262, 495, 512, 528, 548] [212, 215, 248, 263, 496, 513, 529, 549] [213, 216, 249, 264, 497, 514, 530, 550] [214, 217, 250, 265, 498, 515, 531, 551] [215, 218, 251, 266, 499, 516, 532, 552] [216, 219, 252, 267, 500, 517, 533, 553] [217, 220, 253, 268, 501, 518, 534, 554] [227, 230, 263, 272, 511, 528, 544, 558] [228, 231, 264, 273, 512, 529, 545, 559] [229, 232, 265, 274, 513, 530, 546, 560] [230, 233, 266, 275, 514, 531, 547, 561] [231, 234, 267, 276, 515, 532, 548, 562] [232, 235, 268, 277, 516, 533, 549, 563] [233, 236, 269, 278, 517, 534, 550, 564] [234, 237, 270, 279, 518, 535, 551, 565] [2, 35, 283, 300, 336] [14, 50, 65, 298, 315, 331] [1, 34, 335] [15, 66, 299, 316, 332] [0, 334] [16, 67, 333] [19, 52, 300, 317, 353] [31, 67, 82, 315, 332, 348] [18, 51, 352] [32, 83, 316, 333, 349] [17, 351] [33, 84, 350] [36, 69, 317, 334, 370] [48, 84, 99, 332, 349, 365] [35, 68, 369] [49, 100, 333, 350, 366] [34, 368] [50, 101, 367] [53, 86, 334, 351, 387] [65, 101, 116, 349, 366, 382] [52, 85, 386] [66, 117, 350, 367, 383] [51, 385] [67, 118, 384] [70, 103, 351, 368, 404] [82, 118, 133, 366, 383, 399] [69, 102, 403] [83, 134, 367, 384, 400] [68, 402] [84, 135, 401] [87, 120, 368, 385, 421] [99, 135, 150, 383, 400, 416] [86, 119, 420] [100, 151, 384, 401, 417] [85, 419] [101, 152, 418] [104, 137, 385, 402, 438] [116, 152, 167, 400, 417, 433] [103, 136, 437] [117, 168, 401, 418, 434] [102, 436] [118, 169, 435] [121, 154, 402, 419, 455] [133, 169, 184, 417, 434, 450] [120, 153, 454] [134, 185, 418, 435, 451] [119, 453] [135, 186, 452] [138, 171, 419, 436, 472] [150, 186, 201, 434, 451, 467] [137, 170, 471] [151, 202, 435, 452, 468] [136, 470] [152, 203, 469] [155, 188, 436, 453, 489] [167, 203, 218, 451, 468, 484] [154, 187, 488] [168, 219, 452, 469, 485] [153, 487] [169, 220, 486] [172, 205, 453, 470, 506] [184, 220, 235, 468, 485, 501] [171, 204, 505] [185, 236, 469, 486, 502] [170, 504] [186, 237, 503] [189, 222, 470, 487, 523] [201, 237, 252, 485, 502, 518] [188, 221, 522] [202, 253, 486, 503, 519] [187, 521] [203, 254, 520] [206, 239, 487, 504, 540] [218, 254, 269, 502, 519, 535] [205, 238, 539] [219, 270, 503, 520, 536] [204, 538] [220, 271, 537] [223, 256, 504, 521, 557] [235, 271, 280, 519, 536, 552] [222, 255, 556] [236, 281, 520, 537, 553] [221, 555] [237, 282, 554]
H_Z (274 checks, sparse supports)
[0, 20, 36, 53, 286, 301, 334, 337] [1, 21, 37, 54, 287, 302, 335, 338] [2, 22, 38, 55, 288, 303, 336, 339] [3, 23, 39, 56, 289, 304, 337, 340] [4, 24, 40, 57, 290, 305, 338, 341] [5, 25, 41, 58, 291, 306, 339, 342] [6, 26, 42, 59, 292, 307, 340, 343] [7, 27, 43, 60, 293, 308, 341, 344] [8, 28, 44, 61, 294, 309, 342, 345] [9, 29, 45, 62, 295, 310, 343, 346] [10, 30, 46, 63, 296, 311, 344, 347] [11, 31, 47, 64, 297, 312, 345, 348] [12, 32, 48, 65, 298, 313, 346, 349] [13, 33, 49, 66, 299, 314, 347, 350] [17, 37, 53, 70, 303, 318, 351, 354] [18, 38, 54, 71, 304, 319, 352, 355] [19, 39, 55, 72, 305, 320, 353, 356] [20, 40, 56, 73, 306, 321, 354, 357] [21, 41, 57, 74, 307, 322, 355, 358] [22, 42, 58, 75, 308, 323, 356, 359] [23, 43, 59, 76, 309, 324, 357, 360] [24, 44, 60, 77, 310, 325, 358, 361] [25, 45, 61, 78, 311, 326, 359, 362] [26, 46, 62, 79, 312, 327, 360, 363] [27, 47, 63, 80, 313, 328, 361, 364] [28, 48, 64, 81, 314, 329, 362, 365] [29, 49, 65, 82, 315, 330, 363, 366] [30, 50, 66, 83, 316, 331, 364, 367] [34, 54, 70, 87, 320, 335, 368, 371] [35, 55, 71, 88, 321, 336, 369, 372] [36, 56, 72, 89, 322, 337, 370, 373] [37, 57, 73, 90, 323, 338, 371, 374] [38, 58, 74, 91, 324, 339, 372, 375] [39, 59, 75, 92, 325, 340, 373, 376] [40, 60, 76, 93, 326, 341, 374, 377] [41, 61, 77, 94, 327, 342, 375, 378] [42, 62, 78, 95, 328, 343, 376, 379] [43, 63, 79, 96, 329, 344, 377, 380] [44, 64, 80, 97, 330, 345, 378, 381] [45, 65, 81, 98, 331, 346, 379, 382] [46, 66, 82, 99, 332, 347, 380, 383] [47, 67, 83, 100, 333, 348, 381, 384] [51, 71, 87, 104, 337, 352, 385, 388] [52, 72, 88, 105, 338, 353, 386, 389] [53, 73, 89, 106, 339, 354, 387, 390] [54, 74, 90, 107, 340, 355, 388, 391] [55, 75, 91, 108, 341, 356, 389, 392] [56, 76, 92, 109, 342, 357, 390, 393] [57, 77, 93, 110, 343, 358, 391, 394] [58, 78, 94, 111, 344, 359, 392, 395] [59, 79, 95, 112, 345, 360, 393, 396] [60, 80, 96, 113, 346, 361, 394, 397] [61, 81, 97, 114, 347, 362, 395, 398] [62, 82, 98, 115, 348, 363, 396, 399] [63, 83, 99, 116, 349, 364, 397, 400] [64, 84, 100, 117, 350, 365, 398, 401] [68, 88, 104, 121, 354, 369, 402, 405] [69, 89, 105, 122, 355, 370, 403, 406] [70, 90, 106, 123, 356, 371, 404, 407] [71, 91, 107, 124, 357, 372, 405, 408] [72, 92, 108, 125, 358, 373, 406, 409] [73, 93, 109, 126, 359, 374, 407, 410] [74, 94, 110, 127, 360, 375, 408, 411] [75, 95, 111, 128, 361, 376, 409, 412] [76, 96, 112, 129, 362, 377, 410, 413] [77, 97, 113, 130, 363, 378, 411, 414] [78, 98, 114, 131, 364, 379, 412, 415] [79, 99, 115, 132, 365, 380, 413, 416] [80, 100, 116, 133, 366, 381, 414, 417] [81, 101, 117, 134, 367, 382, 415, 418] [85, 105, 121, 138, 371, 386, 419, 422] [86, 106, 122, 139, 372, 387, 420, 423] [87, 107, 123, 140, 373, 388, 421, 424] [88, 108, 124, 141, 374, 389, 422, 425] [89, 109, 125, 142, 375, 390, 423, 426] [90, 110, 126, 143, 376, 391, 424, 427] [91, 111, 127, 144, 377, 392, 425, 428] [92, 112, 128, 145, 378, 393, 426, 429] [93, 113, 129, 146, 379, 394, 427, 430] [94, 114, 130, 147, 380, 395, 428, 431] [95, 115, 131, 148, 381, 396, 429, 432] [96, 116, 132, 149, 382, 397, 430, 433] [97, 117, 133, 150, 383, 398, 431, 434] [98, 118, 134, 151, 384, 399, 432, 435] [102, 122, 138, 155, 388, 403, 436, 439] [103, 123, 139, 156, 389, 404, 437, 440] [104, 124, 140, 157, 390, 405, 438, 441] [105, 125, 141, 158, 391, 406, 439, 442] [106, 126, 142, 159, 392, 407, 440, 443] [107, 127, 143, 160, 393, 408, 441, 444] [108, 128, 144, 161, 394, 409, 442, 445] [109, 129, 145, 162, 395, 410, 443, 446] [110, 130, 146, 163, 396, 411, 444, 447] [111, 131, 147, 164, 397, 412, 445, 448] [112, 132, 148, 165, 398, 413, 446, 449] [113, 133, 149, 166, 399, 414, 447, 450] [114, 134, 150, 167, 400, 415, 448, 451] [115, 135, 151, 168, 401, 416, 449, 452] [119, 139, 155, 172, 405, 420, 453, 456] [120, 140, 156, 173, 406, 421, 454, 457] [121, 141, 157, 174, 407, 422, 455, 458] [122, 142, 158, 175, 408, 423, 456, 459] [123, 143, 159, 176, 409, 424, 457, 460] [124, 144, 160, 177, 410, 425, 458, 461] [125, 145, 161, 178, 411, 426, 459, 462] [126, 146, 162, 179, 412, 427, 460, 463] [127, 147, 163, 180, 413, 428, 461, 464] [128, 148, 164, 181, 414, 429, 462, 465] [129, 149, 165, 182, 415, 430, 463, 466] [130, 150, 166, 183, 416, 431, 464, 467] [131, 151, 167, 184, 417, 432, 465, 468] [132, 152, 168, 185, 418, 433, 466, 469] [136, 156, 172, 189, 422, 437, 470, 473] [137, 157, 173, 190, 423, 438, 471, 474] [138, 158, 174, 191, 424, 439, 472, 475] [139, 159, 175, 192, 425, 440, 473, 476] [140, 160, 176, 193, 426, 441, 474, 477] [141, 161, 177, 194, 427, 442, 475, 478] [142, 162, 178, 195, 428, 443, 476, 479] [143, 163, 179, 196, 429, 444, 477, 480] [144, 164, 180, 197, 430, 445, 478, 481] [145, 165, 181, 198, 431, 446, 479, 482] [146, 166, 182, 199, 432, 447, 480, 483] [147, 167, 183, 200, 433, 448, 481, 484] [148, 168, 184, 201, 434, 449, 482, 485] [149, 169, 185, 202, 435, 450, 483, 486] [153, 173, 189, 206, 439, 454, 487, 490] [154, 174, 190, 207, 440, 455, 488, 491] [155, 175, 191, 208, 441, 456, 489, 492] [156, 176, 192, 209, 442, 457, 490, 493] [157, 177, 193, 210, 443, 458, 491, 494] [158, 178, 194, 211, 444, 459, 492, 495] [159, 179, 195, 212, 445, 460, 493, 496] [160, 180, 196, 213, 446, 461, 494, 497] [161, 181, 197, 214, 447, 462, 495, 498] [162, 182, 198, 215, 448, 463, 496, 499] [163, 183, 199, 216, 449, 464, 497, 500] [164, 184, 200, 217, 450, 465, 498, 501] [165, 185, 201, 218, 451, 466, 499, 502] [166, 186, 202, 219, 452, 467, 500, 503] [170, 190, 206, 223, 456, 471, 504, 507] [171, 191, 207, 224, 457, 472, 505, 508] [172, 192, 208, 225, 458, 473, 506, 509] [173, 193, 209, 226, 459, 474, 507, 510] [174, 194, 210, 227, 460, 475, 508, 511] [175, 195, 211, 228, 461, 476, 509, 512] [176, 196, 212, 229, 462, 477, 510, 513] [177, 197, 213, 230, 463, 478, 511, 514] [178, 198, 214, 231, 464, 479, 512, 515] [179, 199, 215, 232, 465, 480, 513, 516] [180, 200, 216, 233, 466, 481, 514, 517] [181, 201, 217, 234, 467, 482, 515, 518] [182, 202, 218, 235, 468, 483, 516, 519] [183, 203, 219, 236, 469, 484, 517, 520] [187, 207, 223, 240, 473, 488, 521, 524] [188, 208, 224, 241, 474, 489, 522, 525] [189, 209, 225, 242, 475, 490, 523, 526] [190, 210, 226, 243, 476, 491, 524, 527] [191, 211, 227, 244, 477, 492, 525, 528] [192, 212, 228, 245, 478, 493, 526, 529] [193, 213, 229, 246, 479, 494, 527, 530] [194, 214, 230, 247, 480, 495, 528, 531] [195, 215, 231, 248, 481, 496, 529, 532] [196, 216, 232, 249, 482, 497, 530, 533] [197, 217, 233, 250, 483, 498, 531, 534] [198, 218, 234, 251, 484, 499, 532, 535] [199, 219, 235, 252, 485, 500, 533, 536] [200, 220, 236, 253, 486, 501, 534, 537] [204, 224, 240, 257, 490, 505, 538, 541] [205, 225, 241, 258, 491, 506, 539, 542] [206, 226, 242, 259, 492, 507, 540, 543] [207, 227, 243, 260, 493, 508, 541, 544] [208, 228, 244, 261, 494, 509, 542, 545] [209, 229, 245, 262, 495, 510, 543, 546] [210, 230, 246, 263, 496, 511, 544, 547] [211, 231, 247, 264, 497, 512, 545, 548] [212, 232, 248, 265, 498, 513, 546, 549] [213, 233, 249, 266, 499, 514, 547, 550] [214, 234, 250, 267, 500, 515, 548, 551] [215, 235, 251, 268, 501, 516, 549, 552] [216, 236, 252, 269, 502, 517, 550, 553] [217, 237, 253, 270, 503, 518, 551, 554] [221, 241, 257, 507, 522, 555] [222, 242, 258, 508, 523, 556] [223, 243, 259, 509, 524, 557] [224, 244, 260, 510, 525] [225, 245, 261, 272, 511, 526] [226, 246, 262, 273, 512, 527] [227, 247, 263, 274, 513, 528, 558] [228, 248, 264, 275, 514, 529, 559] [229, 249, 265, 276, 515, 530, 560] [230, 250, 266, 277, 516, 531, 558, 561] [231, 251, 267, 278, 517, 532, 559, 562] [232, 252, 268, 279, 518, 533, 560, 563] [233, 253, 269, 280, 519, 534, 561, 564] [234, 254, 270, 281, 520, 535, 562, 565] [3, 19, 36, 284, 317, 320] [238, 258, 524, 539] [2, 19, 300, 303] [255, 541, 556] [2, 283, 286] [4, 20, 37, 285, 318, 321] [239, 259, 525, 540] [3, 20, 301, 304] [256, 542, 557] [3, 284, 287] [5, 21, 38, 286, 319, 322] [240, 260, 526, 541] [4, 21, 302, 305] [257, 543] [4, 285, 288] [6, 22, 39, 287, 320, 323] [241, 261, 527, 542] [5, 22, 303, 306] [258, 272, 544] [5, 286, 289] [7, 23, 40, 288, 321, 324] [242, 262, 272, 528, 543] [6, 23, 304, 307] [259, 273, 545] [6, 287, 290] [8, 24, 41, 289, 322, 325] [243, 263, 273, 529, 544] [7, 24, 305, 308] [260, 274, 546] [7, 288, 291] [9, 25, 42, 290, 323, 326] [244, 264, 274, 530, 545] [8, 25, 306, 309] [261, 275, 547] [8, 289, 292] [272, 558] [10, 26, 43, 291, 324, 327] [245, 265, 275, 531, 546] [9, 26, 307, 310] [262, 276, 548] [9, 290, 293] [273, 559] [11, 27, 44, 292, 325, 328] [246, 266, 276, 532, 547] [10, 27, 308, 311] [263, 277, 549, 558] [10, 291, 294] [274, 560] [12, 28, 45, 293, 326, 329] [247, 267, 277, 533, 548] [11, 28, 309, 312] [264, 278, 550, 559] [11, 292, 295] [275, 561] [13, 29, 46, 294, 327, 330] [248, 268, 278, 534, 549] [12, 29, 310, 313] [265, 279, 551, 560] [12, 293, 296] [276, 562] [14, 30, 47, 295, 328, 331] [249, 269, 279, 535, 550] [13, 30, 311, 314] [266, 280, 552, 561] [13, 294, 297] [277, 563] [15, 31, 48, 296, 329, 332] [250, 270, 280, 536, 551] [14, 31, 312, 315] [267, 281, 553, 562] [14, 295, 298] [278, 564] [16, 32, 49, 297, 330, 333] [251, 271, 281, 537, 552] [15, 32, 313, 316] [268, 282, 554, 563] [15, 296, 299] [279, 565]
Code ID 566-18-20 · download JSON · raw on GitHub