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[[400,12,40]] d ≤
n
400
k
12
d
40
kd²/n
48.0
w
12
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 40, d_Z ≤ 40 · w_X = 12, w_Z = 12 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 40 · witness weight 40 (claimed upper_bound)
witness found by @vprusso · ris_gpu · found at 3×108 trials · survived 3×108 trials · 2026-09-21
witness operator (support, 40 qubits)
[1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, 101, 106, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196]
d_Z 40 · witness weight 40 (claimed upper_bound)
witness found by @vprusso · ris_gpu · found at 3×108 trials · survived 3×108 trials · 2026-09-21
witness operator (support, 40 qubits)
[2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137, 142, 147, 152, 157, 162, 167, 172, 177, 182, 187, 192, 197]
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 12 · H_Z 12
qubit degrees H_X 6 · H_Z 6
trapping sets H_X (1,6)×400 (2,8)×800 (3,10)×4400 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,6): 400 (2,8): 800 (2,10): 11600 (3,10): 4400 (3,12): 81000 (3,14): 501000 (3,16): 29600
trapping sets H_Z (1,6)×400 (2,8)×800 (3,10)×4400 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,6): 400 (2,8): 800 (2,10): 11600 (3,10): 4400 (3,12): 81000 (3,14): 501000 (3,16): 29600

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Two-block group-algebra code on Z_20 x Z_10; random weight-6 supports a=[15,191,60,23,185,146], b=[83,148,105,28,194,76]; RIS-screened search over all abelian groups of order 100-200.
model Ox Alpha 1.0 (claimed, not verified)
date 2026-08-23
notes Distance tightened 58 -> 52 on the X side (2026-08-23 CI refutation seed 449933076): the gate's independent deep search found a weight-52 X-logical; it is embedded as the witness. Upper bound only. Tightened again 52 -> 50 on the X side (2026-08-23 local gate re-run seed 534589698): a weight-50 X-logical was found and is embedded as the witness. Upper bound only.
family generalized bicycle (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

[[400,12,40]]: distance revision of the board's [[400,12,50]] entry

Revision history

[[400,12,40]] supersedes the board's [[400,12,50]] entry. The code, its checks, its layout, and its original provenance are unchanged; only the distance claim is corrected. A GPU random-information-set search (verify/ris_gpu.py, recover mode, 300,000,000 trials per side, seed 2027) exhibits a weight-40 X-logical and a weight-40 Z-logical, so the previous witness-backed bound d <= 50 was overstated and the honest parameter set is [[400,12,40]]. The headline falls from kd^2/n = 75.0 to 48.0. Each lighter witness is carried in the entry with the budget it was found at and survived; the other side keeps its original witness where it was not refuted. Distance remains an upper bound, not an exact claim.

Evidence

Every GPU proposal was re-validated on the CPU against the sparse check matrices (in the kernel of the opposite side's checks, outside the row space of its own side) before it was recorded.

| side | claimed | lightest logical found | trials | seed | CPU-verified | |---|---|---|---|---|---| | X | 50 | 40 | 300,000,000 | 2027 | yes | | Z | 56 | 40 | 300,000,000 | 2027 | yes |

The pass that produced this ran the same search over every verified-new entry on the board; this entry is one of the few whose declared distance did not hold.

Original note, with the file paths updated

[[400,12,50]] — weight-6 2BGA over Z_20 × Z_10

Direction & hypothesis

Target cell: weight-9plus × unrestricted (the code's checks are weight 6, so it competes on every weight board including the weight-6 cell). Family: two-block group-algebra (2BGA) codes over abelian groups. The hypothesis came straight from fieldnotes/2026-07-28-gap-campaign-results.md: at weight 6, abelian groups consistently reach higher distance than non-abelian ones, and the earlier campaign only covered orders 60–120 with GAP. This campaign extended to all abelian groups of order 100–200 (208 groups, all invariant-factor types, including cyclic groups of non-product order the kit samplers miss).

What was searched

  • ~1,500 random weight-6 support pairs (a, b) drawn uniformly over the 208

    • abelian groups of order 100–200 (seed 1).

  • Screened with the kit funnel: k ≥ 6, RIS distance estimate at 3,000

    • trials/backend=auto (gf2_fast), scored by kd²/n. 241 candidates passed.

  • Deep re-screen of all 241 survivors at 200,000 trials/side. Screening

    • distances collapsed heavily (e.g. screen d=60 → ≤24), matching the calibration warning in fieldnotes/2026-08-15-dead-ends-and-leads.md.

  • The eight best distinct-parameter survivors were re-searched at

    • 1,000,000 trials/side; five kept efficiency ≥ 25 after that floor.

Evidence trail

Confirmation ladder for this code (Z_20 × Z_10, supports a=[15,191,60,23,185,146], b=[83,148,105,28,194,76]):

| stage | trials | lightest logical | |---|---|---| | screen | 3,000 | d ≤ 62 | | deep screen | 200,000 | d ≤ 54 | | packaging search | 1,000,000 | X-side witness weight 58, Z-side 62 | | first submission (claimed d=56) | CI gate, seed 449933076 | REFUTED: X-side weight-52 logical | | interim claim (d=52) | local gate re-run, seed 534589698 | REFUTED: X-side weight-50 logical | | tightened claim | trusted validator, fresh seeds | no lighter logical found |

The first submission claimed d ≤ 56; CI's independent RIS-fast pass found a weight-52 X-type logical (seed 449933076), and a second independent pass found weight-50 (seed 534589698), which is now embedded as the X-side witness and sets the final claim. Final claim: **witness-backed upper bound, d ≤ 50** (confidence: upper_bound, both sides). Efficiency kd²/n = 12·50²/400 = 75.0. The trusted validator returned passed: true, board_advancing: true for the weight-9plus × unrestricted cell; literature novelty unverified.

Near-misses from the same sweep: [[396,10,≤39]] (its own first packaging was likewise refuted by the gate — see its note); [[384,12,≤54]] (valid but dominated in its cell); [[288,16,≤36]] (advancing). Two candidates that looked strong at 200k trials were refuted at gate time ([[216,10,26]] collapsed to a witnessed 24; an earlier [[288,16]] packaging claimed 36 and was confirmed at 33).

Dead ends

  • 3,000-trial screening distances are unusable as a ranking signal at these

    • sizes: the top-of-screen records lost 10–65% of claimed d at 200k trials.

  • Gate-time refutations are real even after a 1M-trial packaging floor: this

    • very code's packaging witness (X ≤ 58) did not survive the gate's deeper independent search (→ 52), and a further pass found 50.

  • Low-efficiency tail: most of the 241 screened survivors fell below

    • kd²/n = 15 once distances were honest; the productive region was N = 160–200 with two- or three-factor invariant types.

  • Weight-6 2BGA on small factors (e.g. Z_6×Z_3×Z_3×Z_3) gave high k but

    • d ≤ 18, capping efficiency near 26 despite k up to 26.

Tools

Model: Ox Alpha 1.0 (Zed coding agent). Repo tooling: research/kit/group_algebra.py, research/kit/search.py, research/kit/surrogate.py, research/kit/submit.py, the gf2_fast RIS backend (make fast artifact, 8 threads), and the trusted gate verify/validate_candidate.py. Approximate compute: ~1.5k screening codes + ~250 × 200k-trial + 8 × 1M-trial confirmations on an Apple M-series laptop.

Reproduction

The sweep script builds every abelian group of order 100–200 as an invariant-factor product and yields weight-6 random-support 2BGA codes. This exact code:

dims = [20, 10]                      # Z_20 x Z_10, order N=200
a = [15, 191, 60, 23, 185, 146]
b = [83, 148, 105, 28, 194, 76]
HX, HZ = build_2bga(cyclic_product(*dims), a, b)

The submission JSON embeds both witnesses (X: weight 50 from the gate refutations, Z: weight 56 from the packaging search).

Parity checks

X-checks 200 (max weight 12) · Z-checks 200 (max weight 12)
H_X (200 checks, sparse supports)
[19, 44, 70, 97, 145, 152, 221, 301, 314, 328, 398, 399] [0, 45, 71, 98, 146, 153, 222, 302, 315, 329, 380, 399] [1, 46, 72, 99, 147, 154, 223, 303, 316, 330, 380, 381] [2, 47, 73, 80, 148, 155, 224, 304, 317, 331, 381, 382] [3, 48, 74, 81, 149, 156, 225, 305, 318, 332, 382, 383] [4, 49, 75, 82, 150, 157, 226, 306, 319, 333, 383, 384] [5, 50, 76, 83, 151, 158, 227, 300, 307, 334, 384, 385] [6, 51, 77, 84, 152, 159, 228, 301, 308, 335, 385, 386] [7, 52, 78, 85, 140, 153, 229, 302, 309, 336, 386, 387] [8, 53, 79, 86, 141, 154, 230, 303, 310, 337, 387, 388] [9, 54, 60, 87, 142, 155, 231, 304, 311, 338, 388, 389] [10, 55, 61, 88, 143, 156, 232, 305, 312, 339, 389, 390] [11, 56, 62, 89, 144, 157, 233, 306, 313, 320, 390, 391] [12, 57, 63, 90, 145, 158, 234, 307, 314, 321, 391, 392] [13, 58, 64, 91, 146, 159, 235, 308, 315, 322, 392, 393] [14, 59, 65, 92, 140, 147, 236, 309, 316, 323, 393, 394] [15, 40, 66, 93, 141, 148, 237, 310, 317, 324, 394, 395] [16, 41, 67, 94, 142, 149, 238, 311, 318, 325, 395, 396] [17, 42, 68, 95, 143, 150, 239, 312, 319, 326, 396, 397] [18, 43, 69, 96, 144, 151, 220, 300, 313, 327, 397, 398] [39, 64, 90, 117, 165, 172, 218, 219, 241, 321, 334, 348] [20, 65, 91, 118, 166, 173, 200, 219, 242, 322, 335, 349] [21, 66, 92, 119, 167, 174, 200, 201, 243, 323, 336, 350] [22, 67, 93, 100, 168, 175, 201, 202, 244, 324, 337, 351] [23, 68, 94, 101, 169, 176, 202, 203, 245, 325, 338, 352] [24, 69, 95, 102, 170, 177, 203, 204, 246, 326, 339, 353] [25, 70, 96, 103, 171, 178, 204, 205, 247, 320, 327, 354] [26, 71, 97, 104, 172, 179, 205, 206, 248, 321, 328, 355] [27, 72, 98, 105, 160, 173, 206, 207, 249, 322, 329, 356] [28, 73, 99, 106, 161, 174, 207, 208, 250, 323, 330, 357] [29, 74, 80, 107, 162, 175, 208, 209, 251, 324, 331, 358] [30, 75, 81, 108, 163, 176, 209, 210, 252, 325, 332, 359] [31, 76, 82, 109, 164, 177, 210, 211, 253, 326, 333, 340] [32, 77, 83, 110, 165, 178, 211, 212, 254, 327, 334, 341] [33, 78, 84, 111, 166, 179, 212, 213, 255, 328, 335, 342] [34, 79, 85, 112, 160, 167, 213, 214, 256, 329, 336, 343] [35, 60, 86, 113, 161, 168, 214, 215, 257, 330, 337, 344] [36, 61, 87, 114, 162, 169, 215, 216, 258, 331, 338, 345] [37, 62, 88, 115, 163, 170, 216, 217, 259, 332, 339, 346] [38, 63, 89, 116, 164, 171, 217, 218, 240, 320, 333, 347] [59, 84, 110, 137, 185, 192, 238, 239, 261, 341, 354, 368] [40, 85, 111, 138, 186, 193, 220, 239, 262, 342, 355, 369] [41, 86, 112, 139, 187, 194, 220, 221, 263, 343, 356, 370] [42, 87, 113, 120, 188, 195, 221, 222, 264, 344, 357, 371] [43, 88, 114, 121, 189, 196, 222, 223, 265, 345, 358, 372] [44, 89, 115, 122, 190, 197, 223, 224, 266, 346, 359, 373] [45, 90, 116, 123, 191, 198, 224, 225, 267, 340, 347, 374] [46, 91, 117, 124, 192, 199, 225, 226, 268, 341, 348, 375] [47, 92, 118, 125, 180, 193, 226, 227, 269, 342, 349, 376] [48, 93, 119, 126, 181, 194, 227, 228, 270, 343, 350, 377] [49, 94, 100, 127, 182, 195, 228, 229, 271, 344, 351, 378] [50, 95, 101, 128, 183, 196, 229, 230, 272, 345, 352, 379] [51, 96, 102, 129, 184, 197, 230, 231, 273, 346, 353, 360] [52, 97, 103, 130, 185, 198, 231, 232, 274, 347, 354, 361] [53, 98, 104, 131, 186, 199, 232, 233, 275, 348, 355, 362] [54, 99, 105, 132, 180, 187, 233, 234, 276, 349, 356, 363] [55, 80, 106, 133, 181, 188, 234, 235, 277, 350, 357, 364] [56, 81, 107, 134, 182, 189, 235, 236, 278, 351, 358, 365] [57, 82, 108, 135, 183, 190, 236, 237, 279, 352, 359, 366] [58, 83, 109, 136, 184, 191, 237, 238, 260, 340, 353, 367] [5, 12, 79, 104, 130, 157, 258, 259, 281, 361, 374, 388] [6, 13, 60, 105, 131, 158, 240, 259, 282, 362, 375, 389] [7, 14, 61, 106, 132, 159, 240, 241, 283, 363, 376, 390] [8, 15, 62, 107, 133, 140, 241, 242, 284, 364, 377, 391] [9, 16, 63, 108, 134, 141, 242, 243, 285, 365, 378, 392] [10, 17, 64, 109, 135, 142, 243, 244, 286, 366, 379, 393] [11, 18, 65, 110, 136, 143, 244, 245, 287, 360, 367, 394] [12, 19, 66, 111, 137, 144, 245, 246, 288, 361, 368, 395] [0, 13, 67, 112, 138, 145, 246, 247, 289, 362, 369, 396] [1, 14, 68, 113, 139, 146, 247, 248, 290, 363, 370, 397] [2, 15, 69, 114, 120, 147, 248, 249, 291, 364, 371, 398] [3, 16, 70, 115, 121, 148, 249, 250, 292, 365, 372, 399] [4, 17, 71, 116, 122, 149, 250, 251, 293, 366, 373, 380] [5, 18, 72, 117, 123, 150, 251, 252, 294, 367, 374, 381] [6, 19, 73, 118, 124, 151, 252, 253, 295, 368, 375, 382] [0, 7, 74, 119, 125, 152, 253, 254, 296, 369, 376, 383] [1, 8, 75, 100, 126, 153, 254, 255, 297, 370, 377, 384] [2, 9, 76, 101, 127, 154, 255, 256, 298, 371, 378, 385] [3, 10, 77, 102, 128, 155, 256, 257, 299, 372, 379, 386] [4, 11, 78, 103, 129, 156, 257, 258, 280, 360, 373, 387] [25, 32, 99, 124, 150, 177, 208, 278, 279, 301, 381, 394] [26, 33, 80, 125, 151, 178, 209, 260, 279, 302, 382, 395] [27, 34, 81, 126, 152, 179, 210, 260, 261, 303, 383, 396] [28, 35, 82, 127, 153, 160, 211, 261, 262, 304, 384, 397] [29, 36, 83, 128, 154, 161, 212, 262, 263, 305, 385, 398] [30, 37, 84, 129, 155, 162, 213, 263, 264, 306, 386, 399] [31, 38, 85, 130, 156, 163, 214, 264, 265, 307, 380, 387] [32, 39, 86, 131, 157, 164, 215, 265, 266, 308, 381, 388] [20, 33, 87, 132, 158, 165, 216, 266, 267, 309, 382, 389] [21, 34, 88, 133, 159, 166, 217, 267, 268, 310, 383, 390] [22, 35, 89, 134, 140, 167, 218, 268, 269, 311, 384, 391] [23, 36, 90, 135, 141, 168, 219, 269, 270, 312, 385, 392] [24, 37, 91, 136, 142, 169, 200, 270, 271, 313, 386, 393] [25, 38, 92, 137, 143, 170, 201, 271, 272, 314, 387, 394] [26, 39, 93, 138, 144, 171, 202, 272, 273, 315, 388, 395] [20, 27, 94, 139, 145, 172, 203, 273, 274, 316, 389, 396] [21, 28, 95, 120, 146, 173, 204, 274, 275, 317, 390, 397] [22, 29, 96, 121, 147, 174, 205, 275, 276, 318, 391, 398] [23, 30, 97, 122, 148, 175, 206, 276, 277, 319, 392, 399] [24, 31, 98, 123, 149, 176, 207, 277, 278, 300, 380, 393] [45, 52, 119, 144, 170, 197, 201, 214, 228, 298, 299, 321] [46, 53, 100, 145, 171, 198, 202, 215, 229, 280, 299, 322] [47, 54, 101, 146, 172, 199, 203, 216, 230, 280, 281, 323] [48, 55, 102, 147, 173, 180, 204, 217, 231, 281, 282, 324] [49, 56, 103, 148, 174, 181, 205, 218, 232, 282, 283, 325] [50, 57, 104, 149, 175, 182, 206, 219, 233, 283, 284, 326] [51, 58, 105, 150, 176, 183, 200, 207, 234, 284, 285, 327] [52, 59, 106, 151, 177, 184, 201, 208, 235, 285, 286, 328] [40, 53, 107, 152, 178, 185, 202, 209, 236, 286, 287, 329] [41, 54, 108, 153, 179, 186, 203, 210, 237, 287, 288, 330] [42, 55, 109, 154, 160, 187, 204, 211, 238, 288, 289, 331] [43, 56, 110, 155, 161, 188, 205, 212, 239, 289, 290, 332] [44, 57, 111, 156, 162, 189, 206, 213, 220, 290, 291, 333] [45, 58, 112, 157, 163, 190, 207, 214, 221, 291, 292, 334] [46, 59, 113, 158, 164, 191, 208, 215, 222, 292, 293, 335] [40, 47, 114, 159, 165, 192, 209, 216, 223, 293, 294, 336] [41, 48, 115, 140, 166, 193, 210, 217, 224, 294, 295, 337] [42, 49, 116, 141, 167, 194, 211, 218, 225, 295, 296, 338] [43, 50, 117, 142, 168, 195, 212, 219, 226, 296, 297, 339] [44, 51, 118, 143, 169, 196, 200, 213, 227, 297, 298, 320] [17, 65, 72, 139, 164, 190, 221, 234, 248, 318, 319, 341] [18, 66, 73, 120, 165, 191, 222, 235, 249, 300, 319, 342] [19, 67, 74, 121, 166, 192, 223, 236, 250, 300, 301, 343] [0, 68, 75, 122, 167, 193, 224, 237, 251, 301, 302, 344] [1, 69, 76, 123, 168, 194, 225, 238, 252, 302, 303, 345] [2, 70, 77, 124, 169, 195, 226, 239, 253, 303, 304, 346] [3, 71, 78, 125, 170, 196, 220, 227, 254, 304, 305, 347] [4, 72, 79, 126, 171, 197, 221, 228, 255, 305, 306, 348] [5, 60, 73, 127, 172, 198, 222, 229, 256, 306, 307, 349] [6, 61, 74, 128, 173, 199, 223, 230, 257, 307, 308, 350] [7, 62, 75, 129, 174, 180, 224, 231, 258, 308, 309, 351] [8, 63, 76, 130, 175, 181, 225, 232, 259, 309, 310, 352] [9, 64, 77, 131, 176, 182, 226, 233, 240, 310, 311, 353] [10, 65, 78, 132, 177, 183, 227, 234, 241, 311, 312, 354] [11, 66, 79, 133, 178, 184, 228, 235, 242, 312, 313, 355] [12, 60, 67, 134, 179, 185, 229, 236, 243, 313, 314, 356] [13, 61, 68, 135, 160, 186, 230, 237, 244, 314, 315, 357] [14, 62, 69, 136, 161, 187, 231, 238, 245, 315, 316, 358] [15, 63, 70, 137, 162, 188, 232, 239, 246, 316, 317, 359] [16, 64, 71, 138, 163, 189, 220, 233, 247, 317, 318, 340] [10, 37, 85, 92, 159, 184, 241, 254, 268, 338, 339, 361] [11, 38, 86, 93, 140, 185, 242, 255, 269, 320, 339, 362] [12, 39, 87, 94, 141, 186, 243, 256, 270, 320, 321, 363] [13, 20, 88, 95, 142, 187, 244, 257, 271, 321, 322, 364] [14, 21, 89, 96, 143, 188, 245, 258, 272, 322, 323, 365] [15, 22, 90, 97, 144, 189, 246, 259, 273, 323, 324, 366] [16, 23, 91, 98, 145, 190, 240, 247, 274, 324, 325, 367] [17, 24, 92, 99, 146, 191, 241, 248, 275, 325, 326, 368] [18, 25, 80, 93, 147, 192, 242, 249, 276, 326, 327, 369] [19, 26, 81, 94, 148, 193, 243, 250, 277, 327, 328, 370] [0, 27, 82, 95, 149, 194, 244, 251, 278, 328, 329, 371] [1, 28, 83, 96, 150, 195, 245, 252, 279, 329, 330, 372] [2, 29, 84, 97, 151, 196, 246, 253, 260, 330, 331, 373] [3, 30, 85, 98, 152, 197, 247, 254, 261, 331, 332, 374] [4, 31, 86, 99, 153, 198, 248, 255, 262, 332, 333, 375] [5, 32, 80, 87, 154, 199, 249, 256, 263, 333, 334, 376] [6, 33, 81, 88, 155, 180, 250, 257, 264, 334, 335, 377] [7, 34, 82, 89, 156, 181, 251, 258, 265, 335, 336, 378] [8, 35, 83, 90, 157, 182, 252, 259, 266, 336, 337, 379] [9, 36, 84, 91, 158, 183, 240, 253, 267, 337, 338, 360] [4, 30, 57, 105, 112, 179, 261, 274, 288, 358, 359, 381] [5, 31, 58, 106, 113, 160, 262, 275, 289, 340, 359, 382] [6, 32, 59, 107, 114, 161, 263, 276, 290, 340, 341, 383] [7, 33, 40, 108, 115, 162, 264, 277, 291, 341, 342, 384] [8, 34, 41, 109, 116, 163, 265, 278, 292, 342, 343, 385] [9, 35, 42, 110, 117, 164, 266, 279, 293, 343, 344, 386] [10, 36, 43, 111, 118, 165, 260, 267, 294, 344, 345, 387] [11, 37, 44, 112, 119, 166, 261, 268, 295, 345, 346, 388] [12, 38, 45, 100, 113, 167, 262, 269, 296, 346, 347, 389] [13, 39, 46, 101, 114, 168, 263, 270, 297, 347, 348, 390] [14, 20, 47, 102, 115, 169, 264, 271, 298, 348, 349, 391] [15, 21, 48, 103, 116, 170, 265, 272, 299, 349, 350, 392] [16, 22, 49, 104, 117, 171, 266, 273, 280, 350, 351, 393] [17, 23, 50, 105, 118, 172, 267, 274, 281, 351, 352, 394] [18, 24, 51, 106, 119, 173, 268, 275, 282, 352, 353, 395] [19, 25, 52, 100, 107, 174, 269, 276, 283, 353, 354, 396] [0, 26, 53, 101, 108, 175, 270, 277, 284, 354, 355, 397] [1, 27, 54, 102, 109, 176, 271, 278, 285, 355, 356, 398] [2, 28, 55, 103, 110, 177, 272, 279, 286, 356, 357, 399] [3, 29, 56, 104, 111, 178, 260, 273, 287, 357, 358, 380] [24, 50, 77, 125, 132, 199, 201, 281, 294, 308, 378, 379] [25, 51, 78, 126, 133, 180, 202, 282, 295, 309, 360, 379] [26, 52, 79, 127, 134, 181, 203, 283, 296, 310, 360, 361] [27, 53, 60, 128, 135, 182, 204, 284, 297, 311, 361, 362] [28, 54, 61, 129, 136, 183, 205, 285, 298, 312, 362, 363] [29, 55, 62, 130, 137, 184, 206, 286, 299, 313, 363, 364] [30, 56, 63, 131, 138, 185, 207, 280, 287, 314, 364, 365] [31, 57, 64, 132, 139, 186, 208, 281, 288, 315, 365, 366] [32, 58, 65, 120, 133, 187, 209, 282, 289, 316, 366, 367] [33, 59, 66, 121, 134, 188, 210, 283, 290, 317, 367, 368] [34, 40, 67, 122, 135, 189, 211, 284, 291, 318, 368, 369] [35, 41, 68, 123, 136, 190, 212, 285, 292, 319, 369, 370] [36, 42, 69, 124, 137, 191, 213, 286, 293, 300, 370, 371] [37, 43, 70, 125, 138, 192, 214, 287, 294, 301, 371, 372] [38, 44, 71, 126, 139, 193, 215, 288, 295, 302, 372, 373] [39, 45, 72, 120, 127, 194, 216, 289, 296, 303, 373, 374] [20, 46, 73, 121, 128, 195, 217, 290, 297, 304, 374, 375] [21, 47, 74, 122, 129, 196, 218, 291, 298, 305, 375, 376] [22, 48, 75, 123, 130, 197, 219, 292, 299, 306, 376, 377] [23, 49, 76, 124, 131, 198, 200, 280, 293, 307, 377, 378]
H_Z (200 checks, sparse supports)
[21, 22, 92, 106, 119, 199, 201, 268, 275, 323, 350, 376] [22, 23, 93, 100, 107, 180, 202, 269, 276, 324, 351, 377] [23, 24, 94, 101, 108, 181, 203, 270, 277, 325, 352, 378] [24, 25, 95, 102, 109, 182, 204, 271, 278, 326, 353, 379] [25, 26, 96, 103, 110, 183, 205, 272, 279, 327, 354, 360] [26, 27, 97, 104, 111, 184, 206, 260, 273, 328, 355, 361] [27, 28, 98, 105, 112, 185, 207, 261, 274, 329, 356, 362] [28, 29, 99, 106, 113, 186, 208, 262, 275, 330, 357, 363] [29, 30, 80, 107, 114, 187, 209, 263, 276, 331, 358, 364] [30, 31, 81, 108, 115, 188, 210, 264, 277, 332, 359, 365] [31, 32, 82, 109, 116, 189, 211, 265, 278, 333, 340, 366] [32, 33, 83, 110, 117, 190, 212, 266, 279, 334, 341, 367] [33, 34, 84, 111, 118, 191, 213, 260, 267, 335, 342, 368] [34, 35, 85, 112, 119, 192, 214, 261, 268, 336, 343, 369] [35, 36, 86, 100, 113, 193, 215, 262, 269, 337, 344, 370] [36, 37, 87, 101, 114, 194, 216, 263, 270, 338, 345, 371] [37, 38, 88, 102, 115, 195, 217, 264, 271, 339, 346, 372] [38, 39, 89, 103, 116, 196, 218, 265, 272, 320, 347, 373] [20, 39, 90, 104, 117, 197, 219, 266, 273, 321, 348, 374] [20, 21, 91, 105, 118, 198, 200, 267, 274, 322, 349, 375] [19, 41, 42, 112, 126, 139, 221, 288, 295, 343, 370, 396] [0, 42, 43, 113, 120, 127, 222, 289, 296, 344, 371, 397] [1, 43, 44, 114, 121, 128, 223, 290, 297, 345, 372, 398] [2, 44, 45, 115, 122, 129, 224, 291, 298, 346, 373, 399] [3, 45, 46, 116, 123, 130, 225, 292, 299, 347, 374, 380] [4, 46, 47, 117, 124, 131, 226, 280, 293, 348, 375, 381] [5, 47, 48, 118, 125, 132, 227, 281, 294, 349, 376, 382] [6, 48, 49, 119, 126, 133, 228, 282, 295, 350, 377, 383] [7, 49, 50, 100, 127, 134, 229, 283, 296, 351, 378, 384] [8, 50, 51, 101, 128, 135, 230, 284, 297, 352, 379, 385] [9, 51, 52, 102, 129, 136, 231, 285, 298, 353, 360, 386] [10, 52, 53, 103, 130, 137, 232, 286, 299, 354, 361, 387] [11, 53, 54, 104, 131, 138, 233, 280, 287, 355, 362, 388] [12, 54, 55, 105, 132, 139, 234, 281, 288, 356, 363, 389] [13, 55, 56, 106, 120, 133, 235, 282, 289, 357, 364, 390] [14, 56, 57, 107, 121, 134, 236, 283, 290, 358, 365, 391] [15, 57, 58, 108, 122, 135, 237, 284, 291, 359, 366, 392] [16, 58, 59, 109, 123, 136, 238, 285, 292, 340, 367, 393] [17, 40, 59, 110, 124, 137, 239, 286, 293, 341, 368, 394] [18, 40, 41, 111, 125, 138, 220, 287, 294, 342, 369, 395] [39, 61, 62, 132, 146, 159, 216, 241, 308, 315, 363, 390] [20, 62, 63, 133, 140, 147, 217, 242, 309, 316, 364, 391] [21, 63, 64, 134, 141, 148, 218, 243, 310, 317, 365, 392] [22, 64, 65, 135, 142, 149, 219, 244, 311, 318, 366, 393] [23, 65, 66, 136, 143, 150, 200, 245, 312, 319, 367, 394] [24, 66, 67, 137, 144, 151, 201, 246, 300, 313, 368, 395] [25, 67, 68, 138, 145, 152, 202, 247, 301, 314, 369, 396] [26, 68, 69, 139, 146, 153, 203, 248, 302, 315, 370, 397] [27, 69, 70, 120, 147, 154, 204, 249, 303, 316, 371, 398] [28, 70, 71, 121, 148, 155, 205, 250, 304, 317, 372, 399] [29, 71, 72, 122, 149, 156, 206, 251, 305, 318, 373, 380] [30, 72, 73, 123, 150, 157, 207, 252, 306, 319, 374, 381] [31, 73, 74, 124, 151, 158, 208, 253, 300, 307, 375, 382] [32, 74, 75, 125, 152, 159, 209, 254, 301, 308, 376, 383] [33, 75, 76, 126, 140, 153, 210, 255, 302, 309, 377, 384] [34, 76, 77, 127, 141, 154, 211, 256, 303, 310, 378, 385] [35, 77, 78, 128, 142, 155, 212, 257, 304, 311, 379, 386] [36, 78, 79, 129, 143, 156, 213, 258, 305, 312, 360, 387] [37, 60, 79, 130, 144, 157, 214, 259, 306, 313, 361, 388] [38, 60, 61, 131, 145, 158, 215, 240, 307, 314, 362, 389] [59, 81, 82, 152, 166, 179, 210, 236, 261, 328, 335, 383] [40, 82, 83, 153, 160, 167, 211, 237, 262, 329, 336, 384] [41, 83, 84, 154, 161, 168, 212, 238, 263, 330, 337, 385] [42, 84, 85, 155, 162, 169, 213, 239, 264, 331, 338, 386] [43, 85, 86, 156, 163, 170, 214, 220, 265, 332, 339, 387] [44, 86, 87, 157, 164, 171, 215, 221, 266, 320, 333, 388] [45, 87, 88, 158, 165, 172, 216, 222, 267, 321, 334, 389] [46, 88, 89, 159, 166, 173, 217, 223, 268, 322, 335, 390] [47, 89, 90, 140, 167, 174, 218, 224, 269, 323, 336, 391] [48, 90, 91, 141, 168, 175, 219, 225, 270, 324, 337, 392] [49, 91, 92, 142, 169, 176, 200, 226, 271, 325, 338, 393] [50, 92, 93, 143, 170, 177, 201, 227, 272, 326, 339, 394] [51, 93, 94, 144, 171, 178, 202, 228, 273, 320, 327, 395] [52, 94, 95, 145, 172, 179, 203, 229, 274, 321, 328, 396] [53, 95, 96, 146, 160, 173, 204, 230, 275, 322, 329, 397] [54, 96, 97, 147, 161, 174, 205, 231, 276, 323, 330, 398] [55, 97, 98, 148, 162, 175, 206, 232, 277, 324, 331, 399] [56, 98, 99, 149, 163, 176, 207, 233, 278, 325, 332, 380] [57, 80, 99, 150, 164, 177, 208, 234, 279, 326, 333, 381] [58, 80, 81, 151, 165, 178, 209, 235, 260, 327, 334, 382] [79, 101, 102, 172, 186, 199, 203, 230, 256, 281, 348, 355] [60, 102, 103, 173, 180, 187, 204, 231, 257, 282, 349, 356] [61, 103, 104, 174, 181, 188, 205, 232, 258, 283, 350, 357] [62, 104, 105, 175, 182, 189, 206, 233, 259, 284, 351, 358] [63, 105, 106, 176, 183, 190, 207, 234, 240, 285, 352, 359] [64, 106, 107, 177, 184, 191, 208, 235, 241, 286, 340, 353] [65, 107, 108, 178, 185, 192, 209, 236, 242, 287, 341, 354] [66, 108, 109, 179, 186, 193, 210, 237, 243, 288, 342, 355] [67, 109, 110, 160, 187, 194, 211, 238, 244, 289, 343, 356] [68, 110, 111, 161, 188, 195, 212, 239, 245, 290, 344, 357] [69, 111, 112, 162, 189, 196, 213, 220, 246, 291, 345, 358] [70, 112, 113, 163, 190, 197, 214, 221, 247, 292, 346, 359] [71, 113, 114, 164, 191, 198, 215, 222, 248, 293, 340, 347] [72, 114, 115, 165, 192, 199, 216, 223, 249, 294, 341, 348] [73, 115, 116, 166, 180, 193, 217, 224, 250, 295, 342, 349] [74, 116, 117, 167, 181, 194, 218, 225, 251, 296, 343, 350] [75, 117, 118, 168, 182, 195, 219, 226, 252, 297, 344, 351] [76, 118, 119, 169, 183, 196, 200, 227, 253, 298, 345, 352] [77, 100, 119, 170, 184, 197, 201, 228, 254, 299, 346, 353] [78, 100, 101, 171, 185, 198, 202, 229, 255, 280, 347, 354] [6, 19, 99, 121, 122, 192, 223, 250, 276, 301, 368, 375] [0, 7, 80, 122, 123, 193, 224, 251, 277, 302, 369, 376] [1, 8, 81, 123, 124, 194, 225, 252, 278, 303, 370, 377] [2, 9, 82, 124, 125, 195, 226, 253, 279, 304, 371, 378] [3, 10, 83, 125, 126, 196, 227, 254, 260, 305, 372, 379] [4, 11, 84, 126, 127, 197, 228, 255, 261, 306, 360, 373] [5, 12, 85, 127, 128, 198, 229, 256, 262, 307, 361, 374] [6, 13, 86, 128, 129, 199, 230, 257, 263, 308, 362, 375] [7, 14, 87, 129, 130, 180, 231, 258, 264, 309, 363, 376] [8, 15, 88, 130, 131, 181, 232, 259, 265, 310, 364, 377] [9, 16, 89, 131, 132, 182, 233, 240, 266, 311, 365, 378] [10, 17, 90, 132, 133, 183, 234, 241, 267, 312, 366, 379] [11, 18, 91, 133, 134, 184, 235, 242, 268, 313, 360, 367] [12, 19, 92, 134, 135, 185, 236, 243, 269, 314, 361, 368] [0, 13, 93, 135, 136, 186, 237, 244, 270, 315, 362, 369] [1, 14, 94, 136, 137, 187, 238, 245, 271, 316, 363, 370] [2, 15, 95, 137, 138, 188, 239, 246, 272, 317, 364, 371] [3, 16, 96, 138, 139, 189, 220, 247, 273, 318, 365, 372] [4, 17, 97, 120, 139, 190, 221, 248, 274, 319, 366, 373] [5, 18, 98, 120, 121, 191, 222, 249, 275, 300, 367, 374] [12, 26, 39, 119, 141, 142, 243, 270, 296, 321, 388, 395] [13, 20, 27, 100, 142, 143, 244, 271, 297, 322, 389, 396] [14, 21, 28, 101, 143, 144, 245, 272, 298, 323, 390, 397] [15, 22, 29, 102, 144, 145, 246, 273, 299, 324, 391, 398] [16, 23, 30, 103, 145, 146, 247, 274, 280, 325, 392, 399] [17, 24, 31, 104, 146, 147, 248, 275, 281, 326, 380, 393] [18, 25, 32, 105, 147, 148, 249, 276, 282, 327, 381, 394] [19, 26, 33, 106, 148, 149, 250, 277, 283, 328, 382, 395] [0, 27, 34, 107, 149, 150, 251, 278, 284, 329, 383, 396] [1, 28, 35, 108, 150, 151, 252, 279, 285, 330, 384, 397] [2, 29, 36, 109, 151, 152, 253, 260, 286, 331, 385, 398] [3, 30, 37, 110, 152, 153, 254, 261, 287, 332, 386, 399] [4, 31, 38, 111, 153, 154, 255, 262, 288, 333, 380, 387] [5, 32, 39, 112, 154, 155, 256, 263, 289, 334, 381, 388] [6, 20, 33, 113, 155, 156, 257, 264, 290, 335, 382, 389] [7, 21, 34, 114, 156, 157, 258, 265, 291, 336, 383, 390] [8, 22, 35, 115, 157, 158, 259, 266, 292, 337, 384, 391] [9, 23, 36, 116, 158, 159, 240, 267, 293, 338, 385, 392] [10, 24, 37, 117, 140, 159, 241, 268, 294, 339, 386, 393] [11, 25, 38, 118, 140, 141, 242, 269, 295, 320, 387, 394] [32, 46, 59, 139, 161, 162, 208, 215, 263, 290, 316, 341] [33, 40, 47, 120, 162, 163, 209, 216, 264, 291, 317, 342] [34, 41, 48, 121, 163, 164, 210, 217, 265, 292, 318, 343] [35, 42, 49, 122, 164, 165, 211, 218, 266, 293, 319, 344] [36, 43, 50, 123, 165, 166, 212, 219, 267, 294, 300, 345] [37, 44, 51, 124, 166, 167, 200, 213, 268, 295, 301, 346] [38, 45, 52, 125, 167, 168, 201, 214, 269, 296, 302, 347] [39, 46, 53, 126, 168, 169, 202, 215, 270, 297, 303, 348] [20, 47, 54, 127, 169, 170, 203, 216, 271, 298, 304, 349] [21, 48, 55, 128, 170, 171, 204, 217, 272, 299, 305, 350] [22, 49, 56, 129, 171, 172, 205, 218, 273, 280, 306, 351] [23, 50, 57, 130, 172, 173, 206, 219, 274, 281, 307, 352] [24, 51, 58, 131, 173, 174, 200, 207, 275, 282, 308, 353] [25, 52, 59, 132, 174, 175, 201, 208, 276, 283, 309, 354] [26, 40, 53, 133, 175, 176, 202, 209, 277, 284, 310, 355] [27, 41, 54, 134, 176, 177, 203, 210, 278, 285, 311, 356] [28, 42, 55, 135, 177, 178, 204, 211, 279, 286, 312, 357] [29, 43, 56, 136, 178, 179, 205, 212, 260, 287, 313, 358] [30, 44, 57, 137, 160, 179, 206, 213, 261, 288, 314, 359] [31, 45, 58, 138, 160, 161, 207, 214, 262, 289, 315, 340] [52, 66, 79, 159, 181, 182, 228, 235, 283, 310, 336, 361] [53, 60, 67, 140, 182, 183, 229, 236, 284, 311, 337, 362] [54, 61, 68, 141, 183, 184, 230, 237, 285, 312, 338, 363] [55, 62, 69, 142, 184, 185, 231, 238, 286, 313, 339, 364] [56, 63, 70, 143, 185, 186, 232, 239, 287, 314, 320, 365] [57, 64, 71, 144, 186, 187, 220, 233, 288, 315, 321, 366] [58, 65, 72, 145, 187, 188, 221, 234, 289, 316, 322, 367] [59, 66, 73, 146, 188, 189, 222, 235, 290, 317, 323, 368] [40, 67, 74, 147, 189, 190, 223, 236, 291, 318, 324, 369] [41, 68, 75, 148, 190, 191, 224, 237, 292, 319, 325, 370] [42, 69, 76, 149, 191, 192, 225, 238, 293, 300, 326, 371] [43, 70, 77, 150, 192, 193, 226, 239, 294, 301, 327, 372] [44, 71, 78, 151, 193, 194, 220, 227, 295, 302, 328, 373] [45, 72, 79, 152, 194, 195, 221, 228, 296, 303, 329, 374] [46, 60, 73, 153, 195, 196, 222, 229, 297, 304, 330, 375] [47, 61, 74, 154, 196, 197, 223, 230, 298, 305, 331, 376] [48, 62, 75, 155, 197, 198, 224, 231, 299, 306, 332, 377] [49, 63, 76, 156, 198, 199, 225, 232, 280, 307, 333, 378] [50, 64, 77, 157, 180, 199, 226, 233, 281, 308, 334, 379] [51, 65, 78, 158, 180, 181, 227, 234, 282, 309, 335, 360] [1, 2, 72, 86, 99, 179, 248, 255, 303, 330, 356, 381] [2, 3, 73, 80, 87, 160, 249, 256, 304, 331, 357, 382] [3, 4, 74, 81, 88, 161, 250, 257, 305, 332, 358, 383] [4, 5, 75, 82, 89, 162, 251, 258, 306, 333, 359, 384] [5, 6, 76, 83, 90, 163, 252, 259, 307, 334, 340, 385] [6, 7, 77, 84, 91, 164, 240, 253, 308, 335, 341, 386] [7, 8, 78, 85, 92, 165, 241, 254, 309, 336, 342, 387] [8, 9, 79, 86, 93, 166, 242, 255, 310, 337, 343, 388] [9, 10, 60, 87, 94, 167, 243, 256, 311, 338, 344, 389] [10, 11, 61, 88, 95, 168, 244, 257, 312, 339, 345, 390] [11, 12, 62, 89, 96, 169, 245, 258, 313, 320, 346, 391] [12, 13, 63, 90, 97, 170, 246, 259, 314, 321, 347, 392] [13, 14, 64, 91, 98, 171, 240, 247, 315, 322, 348, 393] [14, 15, 65, 92, 99, 172, 241, 248, 316, 323, 349, 394] [15, 16, 66, 80, 93, 173, 242, 249, 317, 324, 350, 395] [16, 17, 67, 81, 94, 174, 243, 250, 318, 325, 351, 396] [17, 18, 68, 82, 95, 175, 244, 251, 319, 326, 352, 397] [18, 19, 69, 83, 96, 176, 245, 252, 300, 327, 353, 398] [0, 19, 70, 84, 97, 177, 246, 253, 301, 328, 354, 399] [0, 1, 71, 85, 98, 178, 247, 254, 302, 329, 355, 380]
Code ID 400-12-40 · download JSON · raw on GitHub