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[[576,148,18]] d ≤
n
576
k
148
d
18
kd²/n
83.25
w
8
X/Z
1

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 18, d_Z ≤ 18 · 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 18 · witness weight 18 (claimed upper_bound)
witness operator (support, 18 qubits)
[27, 50, 132, 174, 235, 241, 258, 273, 285, 308, 320, 386, 418, 430, 464, 475, 498, 509]
d_Z 18 · witness weight 18 (claimed upper_bound)
witness operator (support, 18 qubits)
[45, 98, 108, 145, 173, 228, 247, 310, 315, 345, 425, 472, 484, 489, 537, 549, 556, 561]
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 8 · H_Z 8 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8 · H_Z 8
qubit degrees H_X 3 · H_Z 3
trapping sets H_X (1,3)×576 (2,4)×6048 (3,5)×84672 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 576 (2,4): 6048 (3,5): 84672 (3,7): 12096
trapping sets H_Z (1,3)×576 (2,4)×6048 (3,5)×84672 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 576 (2,4): 6048 (3,5): 84672 (3,7): 12096

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty known parameter set; see provenance notes
construction Pair-partition CPM-PP CSS (Okada-Kasai family, arXiv:2607.14091) at (J,L,P)=(3,8,72): H[i*P+r, j*P+(r-E[i][j]) mod P] = 1 on both sides from the 3x8 circulant exponent arrays E_X, E_Z printed in Maskara et al. arXiv:2610.06749 Appendix F.1 eq. (62). E_X=[[50,69,70,40,5,39,5,0],[32,62,69,51,61,18,6,25],[33,37,30,47,46,63,23,23]], E_Z=[[32,22,29,49,59,48,36,25],[40,67,60,70,69,37,69,30],[53,17,18,29,66,45,11,3]] mod 72. CSS commutation H_X H_Z^T = 0 reproduced from the printed arrays; k recomputed from the binary ranks (rank H_X = rank H_Z = 214, n = 576) and matched the paper's 148; row weight 8 and column weight 3 on both sides. P = 72 is even, a lift size the family's odd-P construction theory does not cover and that no board entry uses; it reaches the family's d=18 eight qubits shorter than the published odd neighbour [[584,150,18]] at P=73.
model Mimo-V2.6-Flash (claimed, not verified)
builds on arXiv:2610.06749, arXiv:2607.14091
date 2026-10-06
notes Known parameters: the [[576,148,18]] triple and the explicit 3x8 circulant exponent arrays are printed in Maskara et al., arXiv:2610.06749, Appendix F.1 eq. (62), as the base code PP576 of a parallel-surgery gadget; that paper reports no new parameters of its own and contributes logical gates rather than codes. This entry is an independent reconstruction and re-measurement from those printed arrays, not a new construction, and origin stays 'submission' because the matrices were rebuilt here rather than copied from a data file. The pair-partition construction the arrays instantiate is Okada-Kasai, arXiv:2607.14091. The claimed distance is a witness-backed upper bound from this repository's own search; no lower-bound certificate for this instance is held here and the paper's exact-distance argument is not reproduced. Two things are genuinely new to the board. First, the lift P=72 is even: every (3,8) pair-partition entry on the board uses an odd prime lift (P = 29,31,37,59,61,71,73,79,83,89,97,101,103,113), because that family's construction theory needs x^P-1 square-free, so the even-lift strip was unsearched. This entry sits between the odd P=71 and P=73 points at 8 qubits shorter than the published [[584,150,18]] at P=73 and 2 logical qubits above [[568,146,18]] at P=71. Second, it dominates no existing board entry and is dominated by none: it joins the weight-8 x unrestricted Pareto frontier as an incomparable point rather than displacing anything. Equivalence checklist: the exact-fingerprint match reported when this entry was built is against this very file, not against a board entry; against the committed board the gate reports exact_duplicate_of: null and wl_equivalent_of: null. No circuit tier: the Z memory at 18 rounds has 442131 error mechanisms, over the 25000 cap, so the entry is submitted code-tier-only and the generator printed that reason.
family pair-partition CPM (a tag, not a ranking)
locality unrestricted (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

[[576,148,18]] — pair-partition CPM-PP at the even lift P=72, rebuilt from the exponent arrays printed in arXiv:2610.06749

Direction & hypothesis

Target cell: CSS, weight-8 × unrestricted, the cell the pair-partition family lives in. The family is the board's strongest weight-8 line (rate ≈ 0.26 at check weight 8, kd²/n above 100 at the top of the cell), and by early October 2026 its (3,8) branch had been mined at *odd prime* lifts almost end to end: P = 29, 31, 37, 59, 61, 71, 73, 79, 83, 89, 97, 101, 103, 113 all have board entries, several of them filed within the previous fortnight. Every one of those is odd. The construction theory behind the family (Okada–Kasai, arXiv:2607.14091, "Research Tip") leans on P being odd — its maximal-minor rank argument needs x^P − 1 square-free — so the whole search programme had been running in an odd-P world without saying so out loud.

The hypothesis: even lifts are an untouched strip of the same family, and where the odd-P rank argument fails there it costs distance, not existence. Maskara et al., arXiv:2610.06749, print the 3×8 circulant exponent arrays for two pair-partition codes they use as surgery base codes, and one of them is PP576 at (J, L, P) = (3, 8, 72) — an even lift, at d = 18, i.e. the same distance the family reaches at the neighbouring odd P = 73 ([[584,150,18]], already on the board) in 8 fewer qubits. Hypothesis confirmed by one instance: even lifts work, and this one is not on the board.

Honesty about scope: this is a literature reproduction, not a search. The arrays are the paper's; the distance is ours. Nothing here is a new construction, and the claim being filed is narrow — that this parameter set reaches the weight-8 × unrestricted Pareto frontier 8 qubits shorter than its published odd neighbour.

What was searched

Nothing, in the sweep sense, and it is worth being blunt about that. The instances came from reading a paper. What *was* run:

  • Structural reproduction. Build H_X, H_Z from the transcribed 3×8

    • arrays, check CSS commutation H_X H_Zᵀ = 0, recompute k = n − rank H_X − rank H_Z from the binary ranks, and read the row and column weight profiles off both sides. For PP576: n = 576, rank H_X = rank H_Z = 214, k = 148 (matching the paper), row weight 8 and column weight 3 on both sides.

  • Witness search, to convert the paper's d = 18 into a claim this repo can

    • stand behind, in two backends. ./qldpc submit runs both: NumPy RIS at trials = 4000, seed = 0, per side — lightest nontrivial logical **18 on the X side, 18 on the Z side** — then an accelerated pass (gf2_fast) at trials = 1000000, pair_depth = 8, 8 threads, which found nothing lighter. Before packaging the same code was screened at NumPy trials = 2000 (seeds 576/577, 1254 s) and at accelerated trials = 20000 and 80000 with pair_depth = 24 and 32; all four rungs read 18 on both sides. The 1M-trial rung is the one that matters: at the cheap budgets this code reads 16, and a 16 filed against a true 18 would be the wrong claim.

  • Refutation gate (verify/validate_candidate.py, unmodified): 8000 RIS

    • trials, seed 1840086489, nothing lighter, not refuted.

  • The circuit tier was not generated: the Z memory at 18 rounds carries

    • 442131 error mechanisms, over the circuit-tier cap of 25000, so the entry is submitted code-tier-only and the reason is printed rather than dropped silently.

The continuation this entry is meant to enable — sweeping even lifts of the (3,8) array for the shortest n at d = 18, and asking whether d ≥ 20 survives at even P at all — has not been run. P = 72 is one hand-picked instance lifted out of a paper, not the output of a sweep.

Evidence trail

| rung | budget | X side | Z side | reading | |---|---|---|---|---| | NumPy RIS (pre-screen) | 2000 trials, seeds 576/577 (1254 s) | 18 | 18 | witness of weight 18 on each side | | accelerated RIS (pre-screen) | 20 000 trials, pair_depth=24 | 18 | 18 | nothing lighter | | accelerated RIS (pre-screen) | 80 000 trials, pair_depth=32 | 18 | 18 | nothing lighter | | NumPy RIS (filed) | 4000 trials, seed 0 | 18 | 18 | the witnesses stored in the entry | | accelerated RIS (filed) | 1 000 000 trials, pair_depth=8, 8 threads | — | — | nothing lighter | | verify/validate_candidate.py refutation | 8000 RIS trials, seed 1840086489 | — | — | not refuted |

Claim filed: d ≤ 18, witness-backed upper bound, on both sides, with the gate finding no lighter logical in 8000 trials. It is *not* d = 18. The paper reports d = 18 and the family's neighbours agree, but this repository holds no lower-bound certificate for this instance, so the entry is filed upper_bound and the board renders d ≤ 18. No rung above proves that no weight-17 logical exists.

Calibration against the neighbours: the catalogue records [[584,150,18]] at (3,8,73) as exact d = 18 after complete exclusion through weight 16 on both sides, and [[472,122,16]] at (3,8,59). The gate placed this entry on the frontier with dominated_by: []: at n = 576 no board entry has k ≥ 148 at d ≥ 18 and w ≤ 8, and [[568,146,18]] at P = 71 — the nearest shorter point — is two qubits lower in k at the same distance.

Dead ends

  • The third code in the same paper cannot be filed. [[1152,580,12]], the

    • rate-½ APM-PP instance, is over the admissibility cap: n = 1152 exceeds both n ≤ 700 and the n ≤ 1000 extended tier. It is the better code in every physical sense and the board has no way to hold it.

  • The paper itself is the main dead end for a leaderboard. Its

    • contribution is chain-map convolution for parallel surgery, a group-symmetry-adapted logical basis, and subgroup programmability. All of that changes gate overhead; none of it changes (n, k, d, w), which is what the tracks rank. So none of it can advance a board, however good it is. What was usable was incidental: two instances printed in an appendix.

  • **Even lifts are not wholly unmined, which is the honest limit of the

    • hypothesis.** [[576,294,12]] at (4,16,36) is an even lift already on the board. So the strip is untouched for (3,8), not for the family as a whole — a sweep should be expected to find even-P points that re-find known design points before it finds new ones.

  • P = 32 from the same appendix was filed as its own PR rather than folded

    • in here, because CI allows one new code per pull request.

Tools

  • Model: Mimo-V2.6-Flash, credited as provenance.model. It read the

    • paper, transcribed the arrays, and drove the repo tooling; the arithmetic and every verdict come from the trusted stack.

  • Harness: interactive agent session against this checkout, `uv run --extra

    • research for the kit and uv run python for verify/`.

  • Repo tooling: research/kit/submit.py (make_submission, which runs the

    • per-side witness search and embeds the operators), research/kit/surrogate.py (distance_rand, distance_rand_witness), research/kit/coordination.py (staging_dir, gate_and_record), and verify/validate_candidate.py — the gate, unmodified; this is a find only because it returned passed: true.

  • Compute: the filed run was trials = 4000 NumPy plus a 1 000 000-trial

    • accelerated pass, ≈ 2 h wall-clock on a machine shared with several other jobs (load average 150-250 throughout). The cheap pre-screen rungs cost 1254 s (NumPy, trials = 2000) and 29 s / 121 s for the accelerated probes. Pre-packaging screening reused the site's own cell and Pareto logic and reported dominated_by: [].

Reproduction

Self-contained: no repository script is needed, and none is cited.

The paper prints both 3×8 exponent arrays for PP576. With P = 72, L = 8, J = 3, and H[i·P + r, j·P + (r − E[i][j]) mod P] = 1 on both sides:

E_X = [[50, 69, 70, 40,  5, 39,  5,  0],
       [32, 62, 69, 51, 61, 18,  6, 25],
       [33, 37, 30, 47, 46, 63, 23, 23]]

E_Z = [[32, 22, 29, 49, 59, 48, 36, 25],
       [40, 67, 60, 70, 69, 37, 69, 30],
       [53, 17, 18, 29, 66, 45, 11,  3]]

That single rule — circulant blocks C_P^s, entry one where r − c = s — is the whole construction. A zero exponent is the identity block, so the zeroes in E_X are meaningful entries, not gaps. It gives H_X, H_Z of shape `216 × 576, H_X H_Zᵀ = 0, rank H_X = rank H_Z = 214, k = 148`, row weight 8, column weight 3.

Source of the arrays: Maskara, Mehta, He, Menon, Bonilla Ataides, Lukin, Zhou, *Efficient Logic with Ultra-High-Rate Quantum Codes*, arXiv:2610.06749, Appendix F.1, eq. (62). The pair-partition construction these arrays instantiate — the (J,L,P) design system, the girth screens, the exact-distance certificates — is Okada–Kasai, arXiv:2607.14091.

Parity checks

X-checks 216 (max weight 8) · Z-checks 216 (max weight 8)
H_X (216 checks, sparse supports)
[22, 75, 146, 248, 355, 393, 499, 504] [23, 76, 147, 249, 356, 394, 500, 505] [24, 77, 148, 250, 357, 395, 501, 506] [25, 78, 149, 251, 358, 396, 502, 507] [26, 79, 150, 252, 359, 397, 503, 508] [27, 80, 151, 253, 288, 398, 432, 509] [28, 81, 152, 254, 289, 399, 433, 510] [29, 82, 153, 255, 290, 400, 434, 511] [30, 83, 154, 256, 291, 401, 435, 512] [31, 84, 155, 257, 292, 402, 436, 513] [32, 85, 156, 258, 293, 403, 437, 514] [33, 86, 157, 259, 294, 404, 438, 515] [34, 87, 158, 260, 295, 405, 439, 516] [35, 88, 159, 261, 296, 406, 440, 517] [36, 89, 160, 262, 297, 407, 441, 518] [37, 90, 161, 263, 298, 408, 442, 519] [38, 91, 162, 264, 299, 409, 443, 520] [39, 92, 163, 265, 300, 410, 444, 521] [40, 93, 164, 266, 301, 411, 445, 522] [41, 94, 165, 267, 302, 412, 446, 523] [42, 95, 166, 268, 303, 413, 447, 524] [43, 96, 167, 269, 304, 414, 448, 525] [44, 97, 168, 270, 305, 415, 449, 526] [45, 98, 169, 271, 306, 416, 450, 527] [46, 99, 170, 272, 307, 417, 451, 528] [47, 100, 171, 273, 308, 418, 452, 529] [48, 101, 172, 274, 309, 419, 453, 530] [49, 102, 173, 275, 310, 420, 454, 531] [50, 103, 174, 276, 311, 421, 455, 532] [51, 104, 175, 277, 312, 422, 456, 533] [52, 105, 176, 278, 313, 423, 457, 534] [53, 106, 177, 279, 314, 424, 458, 535] [54, 107, 178, 280, 315, 425, 459, 536] [55, 108, 179, 281, 316, 426, 460, 537] [56, 109, 180, 282, 317, 427, 461, 538] [57, 110, 181, 283, 318, 428, 462, 539] [58, 111, 182, 284, 319, 429, 463, 540] [59, 112, 183, 285, 320, 430, 464, 541] [60, 113, 184, 286, 321, 431, 465, 542] [61, 114, 185, 287, 322, 360, 466, 543] [62, 115, 186, 216, 323, 361, 467, 544] [63, 116, 187, 217, 324, 362, 468, 545] [64, 117, 188, 218, 325, 363, 469, 546] [65, 118, 189, 219, 326, 364, 470, 547] [66, 119, 190, 220, 327, 365, 471, 548] [67, 120, 191, 221, 328, 366, 472, 549] [68, 121, 192, 222, 329, 367, 473, 550] [69, 122, 193, 223, 330, 368, 474, 551] [70, 123, 194, 224, 331, 369, 475, 552] [71, 124, 195, 225, 332, 370, 476, 553] [0, 125, 196, 226, 333, 371, 477, 554] [1, 126, 197, 227, 334, 372, 478, 555] [2, 127, 198, 228, 335, 373, 479, 556] [3, 128, 199, 229, 336, 374, 480, 557] [4, 129, 200, 230, 337, 375, 481, 558] [5, 130, 201, 231, 338, 376, 482, 559] [6, 131, 202, 232, 339, 377, 483, 560] [7, 132, 203, 233, 340, 378, 484, 561] [8, 133, 204, 234, 341, 379, 485, 562] [9, 134, 205, 235, 342, 380, 486, 563] [10, 135, 206, 236, 343, 381, 487, 564] [11, 136, 207, 237, 344, 382, 488, 565] [12, 137, 208, 238, 345, 383, 489, 566] [13, 138, 209, 239, 346, 384, 490, 567] [14, 139, 210, 240, 347, 385, 491, 568] [15, 140, 211, 241, 348, 386, 492, 569] [16, 141, 212, 242, 349, 387, 493, 570] [17, 142, 213, 243, 350, 388, 494, 571] [18, 143, 214, 244, 351, 389, 495, 572] [19, 72, 215, 245, 352, 390, 496, 573] [20, 73, 144, 246, 353, 391, 497, 574] [21, 74, 145, 247, 354, 392, 498, 575] [40, 82, 147, 237, 299, 414, 498, 551] [41, 83, 148, 238, 300, 415, 499, 552] [42, 84, 149, 239, 301, 416, 500, 553] [43, 85, 150, 240, 302, 417, 501, 554] [44, 86, 151, 241, 303, 418, 502, 555] [45, 87, 152, 242, 304, 419, 503, 556] [46, 88, 153, 243, 305, 420, 432, 557] [47, 89, 154, 244, 306, 421, 433, 558] [48, 90, 155, 245, 307, 422, 434, 559] [49, 91, 156, 246, 308, 423, 435, 560] [50, 92, 157, 247, 309, 424, 436, 561] [51, 93, 158, 248, 310, 425, 437, 562] [52, 94, 159, 249, 311, 426, 438, 563] [53, 95, 160, 250, 312, 427, 439, 564] [54, 96, 161, 251, 313, 428, 440, 565] [55, 97, 162, 252, 314, 429, 441, 566] [56, 98, 163, 253, 315, 430, 442, 567] [57, 99, 164, 254, 316, 431, 443, 568] [58, 100, 165, 255, 317, 360, 444, 569] [59, 101, 166, 256, 318, 361, 445, 570] [60, 102, 167, 257, 319, 362, 446, 571] [61, 103, 168, 258, 320, 363, 447, 572] [62, 104, 169, 259, 321, 364, 448, 573] [63, 105, 170, 260, 322, 365, 449, 574] [64, 106, 171, 261, 323, 366, 450, 575] [65, 107, 172, 262, 324, 367, 451, 504] [66, 108, 173, 263, 325, 368, 452, 505] [67, 109, 174, 264, 326, 369, 453, 506] [68, 110, 175, 265, 327, 370, 454, 507] [69, 111, 176, 266, 328, 371, 455, 508] [70, 112, 177, 267, 329, 372, 456, 509] [71, 113, 178, 268, 330, 373, 457, 510] [0, 114, 179, 269, 331, 374, 458, 511] [1, 115, 180, 270, 332, 375, 459, 512] [2, 116, 181, 271, 333, 376, 460, 513] [3, 117, 182, 272, 334, 377, 461, 514] [4, 118, 183, 273, 335, 378, 462, 515] [5, 119, 184, 274, 336, 379, 463, 516] [6, 120, 185, 275, 337, 380, 464, 517] [7, 121, 186, 276, 338, 381, 465, 518] [8, 122, 187, 277, 339, 382, 466, 519] [9, 123, 188, 278, 340, 383, 467, 520] [10, 124, 189, 279, 341, 384, 468, 521] [11, 125, 190, 280, 342, 385, 469, 522] [12, 126, 191, 281, 343, 386, 470, 523] [13, 127, 192, 282, 344, 387, 471, 524] [14, 128, 193, 283, 345, 388, 472, 525] [15, 129, 194, 284, 346, 389, 473, 526] [16, 130, 195, 285, 347, 390, 474, 527] [17, 131, 196, 286, 348, 391, 475, 528] [18, 132, 197, 287, 349, 392, 476, 529] [19, 133, 198, 216, 350, 393, 477, 530] [20, 134, 199, 217, 351, 394, 478, 531] [21, 135, 200, 218, 352, 395, 479, 532] [22, 136, 201, 219, 353, 396, 480, 533] [23, 137, 202, 220, 354, 397, 481, 534] [24, 138, 203, 221, 355, 398, 482, 535] [25, 139, 204, 222, 356, 399, 483, 536] [26, 140, 205, 223, 357, 400, 484, 537] [27, 141, 206, 224, 358, 401, 485, 538] [28, 142, 207, 225, 359, 402, 486, 539] [29, 143, 208, 226, 288, 403, 487, 540] [30, 72, 209, 227, 289, 404, 488, 541] [31, 73, 210, 228, 290, 405, 489, 542] [32, 74, 211, 229, 291, 406, 490, 543] [33, 75, 212, 230, 292, 407, 491, 544] [34, 76, 213, 231, 293, 408, 492, 545] [35, 77, 214, 232, 294, 409, 493, 546] [36, 78, 215, 233, 295, 410, 494, 547] [37, 79, 144, 234, 296, 411, 495, 548] [38, 80, 145, 235, 297, 412, 496, 549] [39, 81, 146, 236, 298, 413, 497, 550] [39, 107, 186, 241, 314, 369, 481, 553] [40, 108, 187, 242, 315, 370, 482, 554] [41, 109, 188, 243, 316, 371, 483, 555] [42, 110, 189, 244, 317, 372, 484, 556] [43, 111, 190, 245, 318, 373, 485, 557] [44, 112, 191, 246, 319, 374, 486, 558] [45, 113, 192, 247, 320, 375, 487, 559] [46, 114, 193, 248, 321, 376, 488, 560] [47, 115, 194, 249, 322, 377, 489, 561] [48, 116, 195, 250, 323, 378, 490, 562] [49, 117, 196, 251, 324, 379, 491, 563] [50, 118, 197, 252, 325, 380, 492, 564] [51, 119, 198, 253, 326, 381, 493, 565] [52, 120, 199, 254, 327, 382, 494, 566] [53, 121, 200, 255, 328, 383, 495, 567] [54, 122, 201, 256, 329, 384, 496, 568] [55, 123, 202, 257, 330, 385, 497, 569] [56, 124, 203, 258, 331, 386, 498, 570] [57, 125, 204, 259, 332, 387, 499, 571] [58, 126, 205, 260, 333, 388, 500, 572] [59, 127, 206, 261, 334, 389, 501, 573] [60, 128, 207, 262, 335, 390, 502, 574] [61, 129, 208, 263, 336, 391, 503, 575] [62, 130, 209, 264, 337, 392, 432, 504] [63, 131, 210, 265, 338, 393, 433, 505] [64, 132, 211, 266, 339, 394, 434, 506] [65, 133, 212, 267, 340, 395, 435, 507] [66, 134, 213, 268, 341, 396, 436, 508] [67, 135, 214, 269, 342, 397, 437, 509] [68, 136, 215, 270, 343, 398, 438, 510] [69, 137, 144, 271, 344, 399, 439, 511] [70, 138, 145, 272, 345, 400, 440, 512] [71, 139, 146, 273, 346, 401, 441, 513] [0, 140, 147, 274, 347, 402, 442, 514] [1, 141, 148, 275, 348, 403, 443, 515] [2, 142, 149, 276, 349, 404, 444, 516] [3, 143, 150, 277, 350, 405, 445, 517] [4, 72, 151, 278, 351, 406, 446, 518] [5, 73, 152, 279, 352, 407, 447, 519] [6, 74, 153, 280, 353, 408, 448, 520] [7, 75, 154, 281, 354, 409, 449, 521] [8, 76, 155, 282, 355, 410, 450, 522] [9, 77, 156, 283, 356, 411, 451, 523] [10, 78, 157, 284, 357, 412, 452, 524] [11, 79, 158, 285, 358, 413, 453, 525] [12, 80, 159, 286, 359, 414, 454, 526] [13, 81, 160, 287, 288, 415, 455, 527] [14, 82, 161, 216, 289, 416, 456, 528] [15, 83, 162, 217, 290, 417, 457, 529] [16, 84, 163, 218, 291, 418, 458, 530] [17, 85, 164, 219, 292, 419, 459, 531] [18, 86, 165, 220, 293, 420, 460, 532] [19, 87, 166, 221, 294, 421, 461, 533] [20, 88, 167, 222, 295, 422, 462, 534] [21, 89, 168, 223, 296, 423, 463, 535] [22, 90, 169, 224, 297, 424, 464, 536] [23, 91, 170, 225, 298, 425, 465, 537] [24, 92, 171, 226, 299, 426, 466, 538] [25, 93, 172, 227, 300, 427, 467, 539] [26, 94, 173, 228, 301, 428, 468, 540] [27, 95, 174, 229, 302, 429, 469, 541] [28, 96, 175, 230, 303, 430, 470, 542] [29, 97, 176, 231, 304, 431, 471, 543] [30, 98, 177, 232, 305, 360, 472, 544] [31, 99, 178, 233, 306, 361, 473, 545] [32, 100, 179, 234, 307, 362, 474, 546] [33, 101, 180, 235, 308, 363, 475, 547] [34, 102, 181, 236, 309, 364, 476, 548] [35, 103, 182, 237, 310, 365, 477, 549] [36, 104, 183, 238, 311, 366, 478, 550] [37, 105, 184, 239, 312, 367, 479, 551] [38, 106, 185, 240, 313, 368, 480, 552]
H_Z (216 checks, sparse supports)
[40, 122, 187, 239, 301, 384, 468, 551] [41, 123, 188, 240, 302, 385, 469, 552] [42, 124, 189, 241, 303, 386, 470, 553] [43, 125, 190, 242, 304, 387, 471, 554] [44, 126, 191, 243, 305, 388, 472, 555] [45, 127, 192, 244, 306, 389, 473, 556] [46, 128, 193, 245, 307, 390, 474, 557] [47, 129, 194, 246, 308, 391, 475, 558] [48, 130, 195, 247, 309, 392, 476, 559] [49, 131, 196, 248, 310, 393, 477, 560] [50, 132, 197, 249, 311, 394, 478, 561] [51, 133, 198, 250, 312, 395, 479, 562] [52, 134, 199, 251, 313, 396, 480, 563] [53, 135, 200, 252, 314, 397, 481, 564] [54, 136, 201, 253, 315, 398, 482, 565] [55, 137, 202, 254, 316, 399, 483, 566] [56, 138, 203, 255, 317, 400, 484, 567] [57, 139, 204, 256, 318, 401, 485, 568] [58, 140, 205, 257, 319, 402, 486, 569] [59, 141, 206, 258, 320, 403, 487, 570] [60, 142, 207, 259, 321, 404, 488, 571] [61, 143, 208, 260, 322, 405, 489, 572] [62, 72, 209, 261, 323, 406, 490, 573] [63, 73, 210, 262, 324, 407, 491, 574] [64, 74, 211, 263, 325, 408, 492, 575] [65, 75, 212, 264, 326, 409, 493, 504] [66, 76, 213, 265, 327, 410, 494, 505] [67, 77, 214, 266, 328, 411, 495, 506] [68, 78, 215, 267, 329, 412, 496, 507] [69, 79, 144, 268, 330, 413, 497, 508] [70, 80, 145, 269, 331, 414, 498, 509] [71, 81, 146, 270, 332, 415, 499, 510] [0, 82, 147, 271, 333, 416, 500, 511] [1, 83, 148, 272, 334, 417, 501, 512] [2, 84, 149, 273, 335, 418, 502, 513] [3, 85, 150, 274, 336, 419, 503, 514] [4, 86, 151, 275, 337, 420, 432, 515] [5, 87, 152, 276, 338, 421, 433, 516] [6, 88, 153, 277, 339, 422, 434, 517] [7, 89, 154, 278, 340, 423, 435, 518] [8, 90, 155, 279, 341, 424, 436, 519] [9, 91, 156, 280, 342, 425, 437, 520] [10, 92, 157, 281, 343, 426, 438, 521] [11, 93, 158, 282, 344, 427, 439, 522] [12, 94, 159, 283, 345, 428, 440, 523] [13, 95, 160, 284, 346, 429, 441, 524] [14, 96, 161, 285, 347, 430, 442, 525] [15, 97, 162, 286, 348, 431, 443, 526] [16, 98, 163, 287, 349, 360, 444, 527] [17, 99, 164, 216, 350, 361, 445, 528] [18, 100, 165, 217, 351, 362, 446, 529] [19, 101, 166, 218, 352, 363, 447, 530] [20, 102, 167, 219, 353, 364, 448, 531] [21, 103, 168, 220, 354, 365, 449, 532] [22, 104, 169, 221, 355, 366, 450, 533] [23, 105, 170, 222, 356, 367, 451, 534] [24, 106, 171, 223, 357, 368, 452, 535] [25, 107, 172, 224, 358, 369, 453, 536] [26, 108, 173, 225, 359, 370, 454, 537] [27, 109, 174, 226, 288, 371, 455, 538] [28, 110, 175, 227, 289, 372, 456, 539] [29, 111, 176, 228, 290, 373, 457, 540] [30, 112, 177, 229, 291, 374, 458, 541] [31, 113, 178, 230, 292, 375, 459, 542] [32, 114, 179, 231, 293, 376, 460, 543] [33, 115, 180, 232, 294, 377, 461, 544] [34, 116, 181, 233, 295, 378, 462, 545] [35, 117, 182, 234, 296, 379, 463, 546] [36, 118, 183, 235, 297, 380, 464, 547] [37, 119, 184, 236, 298, 381, 465, 548] [38, 120, 185, 237, 299, 382, 466, 549] [39, 121, 186, 238, 300, 383, 467, 550] [32, 77, 156, 218, 291, 395, 435, 546] [33, 78, 157, 219, 292, 396, 436, 547] [34, 79, 158, 220, 293, 397, 437, 548] [35, 80, 159, 221, 294, 398, 438, 549] [36, 81, 160, 222, 295, 399, 439, 550] [37, 82, 161, 223, 296, 400, 440, 551] [38, 83, 162, 224, 297, 401, 441, 552] [39, 84, 163, 225, 298, 402, 442, 553] [40, 85, 164, 226, 299, 403, 443, 554] [41, 86, 165, 227, 300, 404, 444, 555] [42, 87, 166, 228, 301, 405, 445, 556] [43, 88, 167, 229, 302, 406, 446, 557] [44, 89, 168, 230, 303, 407, 447, 558] [45, 90, 169, 231, 304, 408, 448, 559] [46, 91, 170, 232, 305, 409, 449, 560] [47, 92, 171, 233, 306, 410, 450, 561] [48, 93, 172, 234, 307, 411, 451, 562] [49, 94, 173, 235, 308, 412, 452, 563] [50, 95, 174, 236, 309, 413, 453, 564] [51, 96, 175, 237, 310, 414, 454, 565] [52, 97, 176, 238, 311, 415, 455, 566] [53, 98, 177, 239, 312, 416, 456, 567] [54, 99, 178, 240, 313, 417, 457, 568] [55, 100, 179, 241, 314, 418, 458, 569] [56, 101, 180, 242, 315, 419, 459, 570] [57, 102, 181, 243, 316, 420, 460, 571] [58, 103, 182, 244, 317, 421, 461, 572] [59, 104, 183, 245, 318, 422, 462, 573] [60, 105, 184, 246, 319, 423, 463, 574] [61, 106, 185, 247, 320, 424, 464, 575] [62, 107, 186, 248, 321, 425, 465, 504] [63, 108, 187, 249, 322, 426, 466, 505] [64, 109, 188, 250, 323, 427, 467, 506] [65, 110, 189, 251, 324, 428, 468, 507] [66, 111, 190, 252, 325, 429, 469, 508] [67, 112, 191, 253, 326, 430, 470, 509] [68, 113, 192, 254, 327, 431, 471, 510] [69, 114, 193, 255, 328, 360, 472, 511] [70, 115, 194, 256, 329, 361, 473, 512] [71, 116, 195, 257, 330, 362, 474, 513] [0, 117, 196, 258, 331, 363, 475, 514] [1, 118, 197, 259, 332, 364, 476, 515] [2, 119, 198, 260, 333, 365, 477, 516] [3, 120, 199, 261, 334, 366, 478, 517] [4, 121, 200, 262, 335, 367, 479, 518] [5, 122, 201, 263, 336, 368, 480, 519] [6, 123, 202, 264, 337, 369, 481, 520] [7, 124, 203, 265, 338, 370, 482, 521] [8, 125, 204, 266, 339, 371, 483, 522] [9, 126, 205, 267, 340, 372, 484, 523] [10, 127, 206, 268, 341, 373, 485, 524] [11, 128, 207, 269, 342, 374, 486, 525] [12, 129, 208, 270, 343, 375, 487, 526] [13, 130, 209, 271, 344, 376, 488, 527] [14, 131, 210, 272, 345, 377, 489, 528] [15, 132, 211, 273, 346, 378, 490, 529] [16, 133, 212, 274, 347, 379, 491, 530] [17, 134, 213, 275, 348, 380, 492, 531] [18, 135, 214, 276, 349, 381, 493, 532] [19, 136, 215, 277, 350, 382, 494, 533] [20, 137, 144, 278, 351, 383, 495, 534] [21, 138, 145, 279, 352, 384, 496, 535] [22, 139, 146, 280, 353, 385, 497, 536] [23, 140, 147, 281, 354, 386, 498, 537] [24, 141, 148, 282, 355, 387, 499, 538] [25, 142, 149, 283, 356, 388, 500, 539] [26, 143, 150, 284, 357, 389, 501, 540] [27, 72, 151, 285, 358, 390, 502, 541] [28, 73, 152, 286, 359, 391, 503, 542] [29, 74, 153, 287, 288, 392, 432, 543] [30, 75, 154, 216, 289, 393, 433, 544] [31, 76, 155, 217, 290, 394, 434, 545] [19, 127, 198, 259, 294, 387, 493, 573] [20, 128, 199, 260, 295, 388, 494, 574] [21, 129, 200, 261, 296, 389, 495, 575] [22, 130, 201, 262, 297, 390, 496, 504] [23, 131, 202, 263, 298, 391, 497, 505] [24, 132, 203, 264, 299, 392, 498, 506] [25, 133, 204, 265, 300, 393, 499, 507] [26, 134, 205, 266, 301, 394, 500, 508] [27, 135, 206, 267, 302, 395, 501, 509] [28, 136, 207, 268, 303, 396, 502, 510] [29, 137, 208, 269, 304, 397, 503, 511] [30, 138, 209, 270, 305, 398, 432, 512] [31, 139, 210, 271, 306, 399, 433, 513] [32, 140, 211, 272, 307, 400, 434, 514] [33, 141, 212, 273, 308, 401, 435, 515] [34, 142, 213, 274, 309, 402, 436, 516] [35, 143, 214, 275, 310, 403, 437, 517] [36, 72, 215, 276, 311, 404, 438, 518] [37, 73, 144, 277, 312, 405, 439, 519] [38, 74, 145, 278, 313, 406, 440, 520] [39, 75, 146, 279, 314, 407, 441, 521] [40, 76, 147, 280, 315, 408, 442, 522] [41, 77, 148, 281, 316, 409, 443, 523] [42, 78, 149, 282, 317, 410, 444, 524] [43, 79, 150, 283, 318, 411, 445, 525] [44, 80, 151, 284, 319, 412, 446, 526] [45, 81, 152, 285, 320, 413, 447, 527] [46, 82, 153, 286, 321, 414, 448, 528] [47, 83, 154, 287, 322, 415, 449, 529] [48, 84, 155, 216, 323, 416, 450, 530] [49, 85, 156, 217, 324, 417, 451, 531] [50, 86, 157, 218, 325, 418, 452, 532] [51, 87, 158, 219, 326, 419, 453, 533] [52, 88, 159, 220, 327, 420, 454, 534] [53, 89, 160, 221, 328, 421, 455, 535] [54, 90, 161, 222, 329, 422, 456, 536] [55, 91, 162, 223, 330, 423, 457, 537] [56, 92, 163, 224, 331, 424, 458, 538] [57, 93, 164, 225, 332, 425, 459, 539] [58, 94, 165, 226, 333, 426, 460, 540] [59, 95, 166, 227, 334, 427, 461, 541] [60, 96, 167, 228, 335, 428, 462, 542] [61, 97, 168, 229, 336, 429, 463, 543] [62, 98, 169, 230, 337, 430, 464, 544] [63, 99, 170, 231, 338, 431, 465, 545] [64, 100, 171, 232, 339, 360, 466, 546] [65, 101, 172, 233, 340, 361, 467, 547] [66, 102, 173, 234, 341, 362, 468, 548] [67, 103, 174, 235, 342, 363, 469, 549] [68, 104, 175, 236, 343, 364, 470, 550] [69, 105, 176, 237, 344, 365, 471, 551] [70, 106, 177, 238, 345, 366, 472, 552] [71, 107, 178, 239, 346, 367, 473, 553] [0, 108, 179, 240, 347, 368, 474, 554] [1, 109, 180, 241, 348, 369, 475, 555] [2, 110, 181, 242, 349, 370, 476, 556] [3, 111, 182, 243, 350, 371, 477, 557] [4, 112, 183, 244, 351, 372, 478, 558] [5, 113, 184, 245, 352, 373, 479, 559] [6, 114, 185, 246, 353, 374, 480, 560] [7, 115, 186, 247, 354, 375, 481, 561] [8, 116, 187, 248, 355, 376, 482, 562] [9, 117, 188, 249, 356, 377, 483, 563] [10, 118, 189, 250, 357, 378, 484, 564] [11, 119, 190, 251, 358, 379, 485, 565] [12, 120, 191, 252, 359, 380, 486, 566] [13, 121, 192, 253, 288, 381, 487, 567] [14, 122, 193, 254, 289, 382, 488, 568] [15, 123, 194, 255, 290, 383, 489, 569] [16, 124, 195, 256, 291, 384, 490, 570] [17, 125, 196, 257, 292, 385, 491, 571] [18, 126, 197, 258, 293, 386, 492, 572]
Code ID 576-148-18 · download JSON · raw on GitHub