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[[658,380,8]] d ≤
n
658
k
380
d
8
kd²/n
36.96
w
14
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 8, d_Z ≤ 8 · w_X = 14, w_Z = 14 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[174, 356, 361, 435, 440, 520, 587, 629]
d_Z 8 · witness weight 8 (claimed upper_bound)
witness operator (support, 8 qubits)
[2, 43, 85, 128, 333, 344, 377, 645]
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 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 14 · H_Z 14
qubit degrees H_X 3 · H_Z 3
trapping sets H_X (1,3)×658 (2,4)×12831 (3,3)×1692 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 658 (2,4): 12831 (3,3): 1692 (3,5): 328530 (3,7): 51324
trapping sets H_Z (1,3)×658 (2,4)×12831 (3,3)×1692 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 658 (2,4): 12831 (3,3): 1692 (3,5): 328530 (3,7): 51324

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction CPM pair-partition CSS code (Okada-Kasai family, arXiv:2607.14091) under the symplectic-halving constraint of arXiv:2609.30069 Prop. 4 (eta = -1). (J,L,P)=(3,14,47), n = L*P = 658. Block (i,l) of H_X is the P x P circulant permutation matrix C(E[i][l]) with H_X[i*P+r, l*P+c] = 1 iff c = (r - E[i][l]) mod 47, and H_Z is the same with D[j][l] = -E[j][sigma(l)] mod 47, where sigma(l) = l=0->7, l=1->8, l=2->12, l=3->10, l=4->13, l=5->11, l=6->9, l=7->0, l=8->1, l=9->6, l=10->3, l=11->5, l=12->2, l=13->4. E = [[30, 36, 39, 11, 17, 19, 15, 12, 31, 29, 32, 10, 3, 29], [33, 19, 6, 23, 1, 46, 13, 25, 9, 3, 39, 11, 3, 1], [28, 26, 43, 14, 14, 4, 32, 13, 23, 25, 1, 39, 18, 41]].
model Space Bunny Alpha 1.0 (claimed, not verified)
builds on arXiv:2609.30069, arXiv:2607.14091
date 2026-10-01
notes The CSS parent of a symplectic-halved draw; its fold S = (A | B) on 329 qubits is submitted as a stabilizer-board entry. Solved in the pair-partition null space and hill-climbed inside it. Equivalence to an existing entry was checked by the trusted gate (exact-duplicate and WL-equivalent both null). Literature novelty unverified. Distances are witness-backed upper bounds, not exact certificates.
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

[[658,380,8]] — halving-constrained CPM pair-partition parent

Direction & hypothesis

Target: the stabilizer board for the fold and the **weight-9plus / unrestricted** cell for the parent. The structural lever is symplectic doubling/halving (arXiv:2609.30069 Prop. 4), recorded for this repo in fieldnotes/2026-09-28-symplectic-doubling-and-halving.md: any general stabilizer code S = (A | B) doubles to a CSS code H'_X = (A | B), H'_Z = (B | A) with n -> 2n, k -> 2k and d' >= d, and a CSS code in the CPM pair-partition family halves back out to a genuinely non-CSS code at half the blocklength and half the logicals.

The arithmetic that decided the parameters: a fold's efficiency is k d^2 / n = rate * d^2 with rate = 1 - 2J/L, because n_fold = LP/2 and k_fold ~ P(L/2 - J). The board's existing pair-partition entries sit at (J,L) = (3,8), i.e. rate 1/4, so they leave a factor of ~4 on the table in rate alone. Raising L at fixed J = 3 is the cheap direction, and it is what this draw does.

What was searched

Parameters (J, L, P), eta = -1, sigma a fixed-point-free involution of the L block columns. Construction, per the recipe: block (i,l) of H_X is the P x P circulant permutation matrix C(E[i][l]), i.e. H_X[i*P+r, l*P+c] = 1 iff c = (r - E[i][l]) mod P, and H_Z is the same with D[j][l] = -E[j][sigma(l)] mod P.

  • Draw rates were measured over (J,L) in {(2,6),(2,8),(2,10),(3,8),(3,10),

    • (3,12),(4,8),(4,10),(4,12),(5,12),(5,14),(6,16)} and primes P in {31,47,71}: 12 matchings x 40 draws each. Non-degenerate rate rises with the null-space dimension and collapses for J >= 5, which is always degenerate under the halving constraint (nullity 10-14 against J*L variables).

  • Each surviving draw was hill-climbed for 1500-2000 moves inside the null

    • space of the pair-partition system, minimising 1000*c4 + 30*c6 + c8 where c4, c6, c8 are exact Tanner 4-, 6- and 8-cycle counts on the exponent array. Every move is E <- E + c*b for a null-space basis vector b, so a move cannot break the CSS condition or the halving identity.

  • Two screens were needed and they are not interchangeable. gf2_fast is

    • correct for the CSS sides (it minimises Hamming weight, which *is* the CSS distance). It is not correct for the fold: that side is a Pauli weight where a Y counts once, and the accelerator's doubled Hamming weight counts it twice. Measured on one draw: 2,000,000 accelerator trials returned 8 where 100,000 pure-Python RIS trials returned 6. So the fold used verify/heuristic_distance.py's Pauli-weight RIS under a 1500 s wall-clock cap, and the parent used the accelerator.

  • Screening was ranked on the parent ((3, 14, 47) family, primes 31/47/71) and

    • only the finalists spent the Python budget. Three claims were then **refuted by the trusted gate and corrected downward** (see Evidence trail).

The submitted instance, in full: E = [[30, 36, 39, 11, 17, 19, 15, 12, 31, 29, 32, 10, 3, 29], [33, 19, 6, 23, 1, 46, 13, 25, 9, 3, 39, 11, 3, 1], [28, 26, 43, 14, 14, 4, 32, 13, 23, 25, 1, 39, 18, 41]], sigma = [7, 8, 12, 10, 13, 11, 9, 0, 1, 6, 3, 5, 2, 4].

Evidence trail

CSS parent [[658,380,8]] folds to its symplectic doubling, the stabilizer fold [[329,190,6]]. All distances are witness-backed upper bounds; none is an exact certificate.

  • Parent screen: 380 logicals at d <= 8, then a

    • 400,000-trial gf2_fast per-side pass (seed 17) for the witnesses carried here.

  • Fold screen: pure-Python Pauli-weight RIS, 1500 s wall-clock cap, seed 7.
  • Trusted gate verify/validate_candidate.py: passed: true,

    • board_advancing: true, empty dominator list, exact_duplicate_of and wl_equivalent_of both null.

  • Resource limits: n = 658 <= 700, max check weight w = 14 <= 32,

    • admissible (qldpc_verify.admissible).

  • Claims corrected after refutation, each re-submitted with the refuting

    • witness promoted to the claim: two [[188,95,4]] folds down to d = 3, and [[355,144,8]] down to d = 7.

Final claim: d <= 8, with a weight-8 both X and Z sides embedded in codes/658-380-8.json.

Dead ends

  • **reflect is not a valid sigma, despite appearing in the fieldnote's

    • builder.** sigma(l) = -l mod L fixes l = 0 and l = L/2, so it is not a fixed-point-free involution and Prop. 4 does not apply. It happens to pass a CSS commutation check (for eta = -1 the diagonal cell value is 0 there) while breaking the fold, which is why it survives a naive screen. Its draw rate of 0.91-0.94 is spurious. Every fixed-point-free involution on L columns is L/2 transpositions and hence a conjugate of the shift, so the fix is to sample a random perfect matching; rates then match shift.

  • High rate collapses the distance. J = 2, L = 8 has fold rate 1/2 and

    • draws fine, but d <= 4 at the parent and d <= 3 on the fold. J = 2 at any L tested gave d <= 4. The optimum is J = 3, L = 10-14.

  • J >= 5 is barren: 0 non-degenerate draws in 480 for (5,12), (5,14)

    • and (6,16) at both P = 31 and P = 47.

  • The blocklength cap. A [[710,288,8]] parent from (3,10,71) is

    • board-advancing but inadmissible: above n = 700 the cap admits only w <= 8, and this family has w = L = 10. Its fold [[355,144,7]] is unaffected and is submitted instead.

  • The accelerator over-claims on the CSS sides too at a small budget: at

    • 400,000 trials per side it returned 4 where the gate's refutation found 3, and 8 where it found 7. Both were corrected.

Tools

Model Space Bunny Alpha 1.0 (self-reported; opencode 1.18.34 agent harness). Repo tooling: verify/gf2_fast.cpp as the accelerator, verify/heuristic_distance.py for the Pauli-weight fold search, research/build_halved_pp.py as the reference implementation of the recipe, and a local re-implementation of its sampler that screens degeneracy in the exponent domain (a (J,L,L) test, since H_X's column (l,c) is {(i, c+E[i][l])} and two columns coincide exactly when E[:,l] - E[:,l'] is constant over i) and counts short cycles exactly. That re-implementation turned a ~20 min/draw search into ~5 s and is not committed here; the recipe above plus the exponent array is sufficient to rebuild the matrices without it. Roughly 6 CPU-hours on a shared, heavily loaded machine.

Reproduction

From E and sigma above, with P = 47:

D[j][l] = -E[j][sigma(l)] mod P
H_X[i*P + r, l*P + (r - E[i][l]) mod P] = 1     for i in 0..2, r in Z_P
H_Z[j*P + r, l*P + (r - D[j][l]) mod P] = 1     for j in 0..2, r in Z_P

verify_css gives H_X H_Z^T = 0. For the fold, let pi(l, t) = (sigma(l), -t mod P) on the L*P columns, order them so each {q, pi(q)} pair is adjacent, then A, B = H_X'[:, :n_f], H_X'[:, n_f:] with n_f = L*P/2 = 329, and the generators of the submitted entry are the rows of S = (A | B). Isotropy A B^T + B A^T = 0 follows from the CSS condition. Generator i carries X on supp A_i and Z on supp B_i; a qubit in both carries Y.

Parity checks

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