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[[396,10,33]] d ≤
n
396
k
10
d
33
kd²/n
27.5
w
12
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 33, d_Z ≤ 33 · 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 33 · witness weight 33 (claimed upper_bound)
witness found by @vprusso · ris_gpu · found at 3×108 trials · survived 3×108 trials · 2026-09-21
witness operator (support, 33 qubits)
[3, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 67, 73, 79, 85, 91, 97, 103, 109, 115, 121, 127, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197]
d_Z 33 · witness weight 33 (claimed upper_bound)
witness found by @vprusso · verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified) · found at 3×108 trials · survived 3×108 trials · 2026-09-25
witness operator (support, 33 qubits)
[71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131, 137, 143, 149, 155, 161, 167, 173, 179, 185, 191, 197, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258]
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)×396 (2,8)×396 (3,6)×66 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,6): 396 (2,8): 396 (2,10): 12276 (3,6): 66 (3,10): 2970 (3,12): 57024 (3,14): 549648 (3,16): 36432
trapping sets H_Z (1,6)×396 (2,8)×396 (3,6)×66 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,6): 396 (2,8): 396 (2,10): 12276 (3,6): 66 (3,10): 2970 (3,12): 57024 (3,14): 549648 (3,16): 36432

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Two-block group-algebra code on Z_66 x Z_3; random weight-6 supports a=[94,190,57,153,59,16], b=[2,190,124,194,134,158]; 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 60 -> 39 on the X side (2026-08-23 CI refutation seed 1882473206): the gate's independent deep search found a weight-39 X-logical; it is embedded as the witness. Upper bound only. Distance tightened 39 -> 37 on the X side (issue #899, 2026-09-05): a weight-37 X-type logical found by verify/heuristic_distance.py at 8,000,000 RIS trials (seed 1) is embedded as the X 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

[[396,10,33]]: distance revision of the board's [[396,10,33]] entry

Revision history

The entry keeps its parameters [[396,10,33]]. The code, its checks, its layout, and its original provenance are unchanged; only the distance block is corrected. A GPU random-information-set search (verify/ris_gpu.py, recover mode, 300,000,000 trials per side, pair depth 0, seed 4102) exhibits a weight-33 Z logical, so the previous witness-backed bound was overstated on that side; the overall distance d = 33 is unchanged. Each lighter witness is carried in the entry with the budget it was found at; 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 committed check matrices (in the kernel of the opposite side's checks, outside the row space of its own side) before it was recorded. The pass is the weekly fresh-seed re-measurement of the board's cell leaders (issue 2025, run of 2026-09-24); every recorded reading is the lightest CPU-verified logical at that budget.

| side | seed | claimed | GPU best weight | CPU-verified witness | trials | |---|---|---|---|---|---| | X | 4101 | 33 | 33 | 33 | 300,000,000 | | Z | 4101 | 48 | 49 | 49 | 300,000,000 | | X | 4102 | 33 | 33 | 33 | 300,000,000 | | Z | 4102 | 48 | 33 | 33 | 300,000,000 |

Original note, with the file paths updated

[[396,10,33]]: distance revision of the board's [[396,10,37]] entry

Revision history

[[396,10,33]] supersedes the board's [[396,10,37]] 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-33 X-logical and a weight-48 Z-logical, so the previous witness-backed bound d <= 37 was overstated and the honest parameter set is [[396,10,33]]. The headline falls from kd^2/n = 34.57 to 27.5. 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 | 37 | 33 | 300,000,000 | 2027 | yes | | Z | 59 | 48 | 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

[[396,10,37]]: weight-6 2BGA over Z_66 × Z_3

Direction & hypothesis

Target cell: weight-9plus × unrestricted (checks are weight 6, so the code also competes on the weight-6 board). Family: two-block group-algebra (2BGA) codes over abelian groups, following fieldnotes/2026-07-28-gap-campaign-results.md: at weight 6, abelian groups consistently reach higher distance than non-abelian ones. This campaign extended that work to all abelian groups of order 100–200 (208 groups, all invariant-factor types).

What was searched

  • ~1,500 random weight-6 support pairs (a, b) over the 208 abelian groups of

    • order 100–200 (seed 1).

  • Screened with the kit funnel: k ≥ 6, RIS at 3,000 trials (gf2_fast),

    • scored by kd²/n. 241 candidates passed.

  • Deep re-screen of all survivors at 200,000 trials/side; screening distances

    • collapsed heavily (screen d=63 → ≤55 for this code).

  • Top survivors re-searched at 1,000,000 trials/side.

Evidence trail

Confirmation ladder (Z_66 × Z_3, a=[94,190,57,153,59,16], b=[2,190,124,194,134,158]):

| stage | trials | lightest logical | |---|---|---| | screen | 3,000 | d ≤ 63 | | deep screen | 200,000 | d ≤ 55 | | packaging search | 1,000,000 | X-side witness weight 60, Z-side 59 | | first submission (claimed d=59) | CI gate, seed 1882473206 | REFUTED: X-side weight-39 logical | | tightened claim | trusted validator, fresh seeds | no lighter logical found |

The first submission claimed d ≤ 59; CI's independent RIS-fast pass found a weight-39 X-type logical (seed 1882473206), which is now embedded as the X-side witness and sets the final claim. Final claim: **witness-backed upper bound (confidence: upper_bound, both sides), packaged at d ≤ 39**. Efficiency kd²/n = 10·39²/396 = 38.41. The trusted validator returned passed: true, board_advancing: true; literature novelty unverified.

Sibling finds from the same sweep: [[400,12,≤52]] and [[288,16,≤36]] (both gate-passed and board-advancing, submitted separately); [[384,12,≤54]] (valid but dominated in its cell).

Dead ends

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

    • sizes (10–65% distance loss at 200k trials across the top records).

  • Gate-time refutations are real even after a 1M-trial floor: this very code's

    • packaging witnesses (X ≤ 60) did not survive the gate's deeper independent search, which found 39 — a much larger collapse than the packaging pass suggested. Sibling candidates were refuted too ([[216,10,26]] → 24, an earlier [[288,16]] packaging → 33).

  • Most screened survivors fell below kd²/n = 15 once distances were honest;

    • the productive region was N = 160–200 with two/three-factor invariant types.

Tools

Model: Ox Alpha 1.0 (Zed agent harness). Repo tooling: research/kit/group_algebra.py, research/kit/search.py, research/kit/surrogate.py, research/kit/submit.py, gf2_fast RIS backend (8 threads), trusted gate verify/validate_candidate.py. Compute: ~1.5k screening codes + ~250 × 200k-trial + 8 × 1M-trial confirmations.

Reproduction

dims = [66, 3]                       # Z_66 x Z_3, order N=198
a = [94, 190, 57, 153, 59, 16]
b = [2, 190, 124, 194, 134, 158]
HX, HZ = build_2bga(cyclic_product(*dims), a, b)

The submission JSON embeds both witnesses (X: weight 39 from the gate refutation, Z: weight 59 from the packaging search).

Second tightening (issue #899)

The X-side claim of 39 did not hold either. verify/heuristic_distance.py at 8,000,000 RIS trials (seed 1) found an X-type logical of weight 37, checked against the entry's own checks (in the kernel of H_Z, syndrome weight 84 against H_X so not a stabiliser, rank 193 against 194 with the operator appended). It is embedded as the X-side witness; the file was renamed to codes/396-10-33.json, distance.d = 37, and the claim stays a witnessed upper bound. Efficiency k d^2 / n = 10 * 37^2 / 396 = 34.57. The evidence table above is left as the record of the first two claims.

Parity checks

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