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[[390,82,30]] d ≤
n
390
k
82
d
30
kd²/n
189.231
w
16

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Distance

d_X 30 · witness weight 30 (claimed upper_bound)
witness operator (support, 30 qubits)
[13, 20, 59, 78, 83, 87, 92, 95, 104, 126, 127, 128, 138, 151, 172, 190, 220, 245, 249, 266, 280, 300, 307, 324, 332, 341, 354, 367, 380, 385]
d_Z 30 · witness weight 30 (claimed upper_bound)
witness operator (support, 30 qubits)
[5, 10, 23, 36, 49, 58, 66, 83, 90, 110, 124, 141, 145, 170, 200, 218, 239, 252, 262, 263, 264, 286, 295, 298, 303, 307, 312, 331, 370, 377]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Generalized bicycle (2BGA on Z_195), circulant size 195, a(x) support {0,34,47,72,78,85,187,193}, b(x) support {0,93,117,136,145,163,187,188}; H_X=[A|B], H_Z=[B^T|A^T]. Check weight 16.
model Claude Claude Fable 5 (claimed, not verified)
builds on arXiv:1904.02703, arXiv:2306.16400
date 2026-07-15
notes Distance upper bound d<=30 from an explicit weight-30 Z logical witness (both sides weight 30; the X witness is the Z witness under the GB transpose symmetry, machine-verified). Refutation evidence: RIS ladders to 8M/side during discovery, then three fresh-seed passes at 80M trials/side (pair-depth 20) all held at 30-31, plus an independent BP+OSD syndrome-decoder pass found nothing lighter than 41; nothing below 30 across ~240M trials and two methods. Upper bound only; exact certification is out of MILP reach at n=390. Literature novelty unverified.
family generalized bicycle (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight > 8 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

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