{ "schema_version": "0.1", "name": "[[324,4,30]] non-abelian 2BGA on dih(81)", "code_type": "CSS", "n": 324, "k": 4, "checks": { "X": [ [ 93, 122, 134, 161, 165, 169, 192, 235, 271, 322 ], [ 89, 126, 138, 157, 168, 173, 196, 231, 267, 318 ], [ 88, 127, 139, 156, 170, 175, 198, 229, 265, 316 ], [ 85, 130, 142, 153, 172, 177, 200, 227, 263, 314 ], [ 84, 131, 143, 152, 167, 171, 194, 233, 269, 320 ], [ 92, 123, 135, 160, 174, 179, 202, 225, 261, 312 ], [ 81, 134, 146, 149, 176, 181, 204, 223, 259, 310 ], [ 80, 135, 147, 148, 162, 164, 190, 237, 273, 323 ], [ 96, 119, 131, 159, 178, 183, 206, 221, 257, 308 ], [ 97, 118, 130, 158, 163, 166, 188, 239, 275, 321 ], [ 77, 138, 145, 150, 180, 185, 208, 219, 255, 306 ], [ 76, 139, 144, 151, 163, 166, 186, 241, 277, 319 ], [ 100, 115, 127, 155, 182, 187, 210, 217, 253, 304 ], [ 101, 114, 126, 154, 162, 164, 184, 243, 279, 317 ], [ 73, 141, 142, 154, 184, 189, 212, 215, 251, 302 ], [ 72, 140, 143, 155, 165, 169, 182, 245, 281, 315 ], [ 104, 111, 123, 151, 186, 191, 213, 214, 249, 300 ], [ 105, 110, 122, 150, 167, 171, 180, 247, 283, 313 ], [ 69, 137, 146, 158, 188, 193, 211, 216, 247, 298 ], [ 68, 136, 147, 159, 168, 173, 178, 249, 285, 311 ], [ 107, 108, 119, 147, 190, 195, 209, 218, 245, 296 ], [ 106, 109, 118, 146, 170, 175, 176, 251, 287, 309 ], [ 65, 133, 150, 161, 192, 197, 207, 220, 243, 294 ], [ 64, 132, 151, 160, 172, 174, 177, 253, 289, 307 ], [ 103, 112, 115, 143, 194, 199, 205, 222, 241, 292 ], [ 102, 113, 114, 142, 172, 174, 179, 255, 291, 305 ], [ 61, 129, 154, 157, 196, 201, 203, 224, 239, 290 ], [ 60, 128, 155, 156, 170, 176, 181, 257, 293, 303 ], [ 99, 111, 116, 139, 198, 201, 203, 226, 237, 288 ], [ 98, 110, 117, 138, 168, 178, 183, 259, 295, 301 ], [ 57, 125, 153, 158, 199, 200, 205, 228, 235, 286 ], [ 56, 124, 152, 159, 167, 180, 185, 261, 297, 299 ], [ 95, 107, 120, 135, 197, 202, 207, 230, 233, 284 ], [ 94, 106, 121, 134, 165, 182, 187, 263, 297, 299 ], [ 53, 121, 149, 161, 195, 204, 209, 231, 232, 282 ], [ 52, 120, 148, 160, 164, 184, 189, 265, 295, 301 ], [ 91, 103, 124, 131, 193, 206, 211, 229, 234, 280 ], [ 90, 102, 125, 130, 163, 186, 191, 267, 293, 303 ], [ 49, 117, 145, 157, 191, 208, 213, 227, 236, 278 ], [ 48, 116, 144, 156, 166, 188, 193, 269, 291, 305 ], [ 87, 99, 127, 128, 189, 210, 215, 225, 238, 276 ], [ 86, 98, 126, 129, 162, 190, 195, 271, 289, 307 ], [ 45, 113, 141, 153, 187, 212, 217, 223, 240, 274 ], [ 44, 112, 140, 152, 169, 192, 197, 273, 287, 309 ], [ 83, 95, 123, 132, 185, 214, 219, 221, 242, 272 ], [ 82, 94, 122, 133, 171, 194, 199, 275, 285, 311 ], [ 41, 109, 137, 149, 183, 216, 219, 221, 244, 270 ], [ 40, 108, 136, 148, 173, 196, 201, 277, 283, 313 ], [ 79, 91, 119, 136, 181, 217, 218, 223, 246, 268 ], [ 78, 90, 118, 137, 175, 198, 203, 279, 281, 315 ], [ 37, 105, 133, 145, 179, 215, 220, 225, 248, 266 ], [ 36, 104, 132, 144, 177, 200, 205, 279, 281, 317 ], [ 75, 87, 115, 140, 177, 213, 222, 227, 250, 264 ], [ 74, 86, 114, 141, 179, 202, 207, 277, 283, 319 ], [ 33, 101, 129, 141, 175, 211, 224, 229, 252, 262 ], [ 32, 100, 128, 140, 181, 204, 209, 275, 285, 321 ], [ 71, 83, 111, 144, 173, 209, 226, 231, 254, 260 ], [ 70, 82, 110, 145, 183, 206, 211, 273, 287, 323 ], [ 29, 97, 125, 137, 171, 207, 228, 233, 256, 258 ], [ 28, 96, 124, 136, 185, 208, 213, 271, 289, 322 ], [ 67, 79, 107, 148, 169, 205, 230, 235, 256, 258 ], [ 66, 78, 106, 149, 187, 210, 215, 269, 291, 320 ], [ 25, 93, 121, 133, 162, 203, 232, 237, 254, 260 ], [ 24, 92, 120, 132, 189, 212, 217, 267, 293, 318 ], [ 63, 75, 103, 152, 166, 201, 234, 239, 252, 262 ], [ 62, 74, 102, 153, 191, 214, 219, 265, 295, 316 ], [ 21, 89, 117, 129, 163, 199, 236, 241, 250, 264 ], [ 20, 88, 116, 128, 193, 216, 221, 263, 297, 314 ], [ 59, 71, 99, 156, 164, 197, 238, 243, 248, 266 ], [ 58, 70, 98, 157, 195, 218, 223, 261, 299, 312 ], [ 17, 85, 113, 125, 165, 195, 240, 245, 246, 268 ], [ 16, 84, 112, 124, 197, 220, 225, 259, 301, 310 ], [ 55, 67, 95, 160, 167, 193, 242, 244, 247, 270 ], [ 54, 66, 94, 161, 199, 222, 227, 257, 303, 308 ], [ 13, 81, 109, 121, 168, 191, 242, 244, 249, 272 ], [ 12, 80, 108, 120, 201, 224, 229, 255, 305, 306 ], [ 51, 63, 91, 159, 170, 189, 240, 246, 251, 274 ], [ 50, 62, 90, 158, 203, 226, 231, 253, 304, 307 ], [ 9, 77, 105, 117, 172, 187, 238, 248, 253, 276 ], [ 8, 76, 104, 116, 205, 228, 233, 251, 302, 309 ], [ 47, 59, 87, 155, 174, 185, 236, 250, 255, 278 ], [ 46, 58, 86, 154, 207, 230, 235, 249, 300, 311 ], [ 0, 73, 101, 113, 176, 183, 234, 252, 257, 280 ], [ 5, 72, 100, 112, 209, 232, 237, 247, 298, 313 ], [ 43, 55, 83, 151, 178, 181, 232, 254, 259, 282 ], [ 42, 54, 82, 150, 211, 234, 239, 245, 296, 315 ], [ 1, 69, 97, 109, 179, 180, 230, 256, 261, 284 ], [ 2, 68, 96, 108, 213, 236, 241, 243, 294, 317 ], [ 39, 51, 79, 147, 177, 182, 228, 258, 263, 286 ], [ 38, 50, 78, 146, 215, 238, 241, 243, 292, 319 ], [ 3, 65, 93, 105, 175, 184, 226, 260, 265, 288 ], [ 4, 64, 92, 104, 217, 239, 240, 245, 290, 321 ], [ 35, 47, 75, 143, 173, 186, 224, 262, 267, 290 ], [ 34, 46, 74, 142, 219, 237, 242, 247, 288, 323 ], [ 6, 61, 89, 101, 171, 188, 222, 264, 269, 292 ], [ 7, 60, 88, 100, 221, 235, 244, 249, 286, 322 ], [ 31, 43, 71, 139, 169, 190, 220, 266, 271, 294 ], [ 30, 42, 70, 138, 223, 233, 246, 251, 284, 320 ], [ 10, 57, 85, 97, 162, 192, 218, 268, 273, 296 ], [ 11, 56, 84, 96, 225, 231, 248, 253, 282, 318 ], [ 27, 39, 67, 135, 166, 194, 216, 270, 275, 298 ], [ 26, 38, 66, 134, 227, 229, 250, 255, 280, 316 ], [ 14, 53, 81, 93, 163, 196, 214, 272, 277, 300 ], [ 15, 52, 80, 92, 227, 229, 252, 257, 278, 314 ], [ 23, 35, 63, 131, 164, 198, 212, 274, 279, 302 ], [ 22, 34, 62, 130, 225, 231, 254, 259, 276, 312 ], [ 18, 49, 77, 89, 165, 200, 210, 276, 281, 304 ], [ 19, 48, 76, 88, 223, 233, 256, 261, 274, 310 ], [ 19, 31, 59, 127, 167, 202, 208, 278, 283, 306 ], [ 18, 30, 58, 126, 221, 235, 258, 263, 272, 308 ], [ 22, 45, 73, 85, 168, 204, 206, 280, 285, 308 ], [ 23, 44, 72, 84, 219, 237, 260, 265, 270, 306 ], [ 15, 27, 55, 123, 170, 204, 206, 282, 287, 310 ], [ 14, 26, 54, 122, 217, 239, 262, 267, 268, 304 ], [ 26, 41, 69, 81, 172, 202, 208, 284, 289, 312 ], [ 27, 40, 68, 80, 215, 241, 264, 266, 269, 302 ], [ 11, 23, 51, 119, 174, 200, 210, 286, 291, 314 ], [ 10, 22, 50, 118, 213, 243, 264, 266, 271, 300 ], [ 30, 37, 65, 77, 176, 198, 212, 288, 293, 316 ], [ 31, 36, 64, 76, 211, 245, 262, 268, 273, 298 ], [ 7, 19, 47, 115, 178, 196, 214, 290, 295, 318 ], [ 6, 18, 46, 114, 209, 247, 260, 270, 275, 296 ], [ 33, 34, 61, 73, 180, 194, 216, 292, 297, 320 ], [ 32, 35, 60, 72, 207, 249, 258, 272, 277, 294 ], [ 4, 15, 43, 111, 182, 192, 218, 294, 299, 322 ], [ 3, 14, 42, 110, 205, 251, 256, 274, 279, 292 ], [ 29, 38, 57, 69, 184, 190, 220, 296, 301, 323 ], [ 28, 39, 56, 68, 203, 253, 254, 276, 281, 290 ], [ 2, 11, 39, 107, 186, 188, 222, 298, 303, 321 ], [ 1, 10, 38, 106, 201, 252, 255, 278, 283, 288 ], [ 25, 42, 53, 65, 186, 188, 224, 300, 305, 319 ], [ 24, 43, 52, 64, 199, 250, 257, 280, 285, 286 ], [ 5, 7, 35, 103, 184, 190, 226, 302, 307, 317 ], [ 0, 6, 34, 102, 197, 248, 259, 282, 284, 287 ], [ 21, 46, 49, 61, 182, 192, 228, 304, 309, 315 ], [ 20, 47, 48, 60, 195, 246, 261, 282, 284, 289 ], [ 4, 8, 31, 99, 180, 194, 230, 306, 311, 313 ], [ 3, 9, 30, 98, 193, 244, 263, 280, 286, 291 ], [ 17, 45, 50, 57, 178, 196, 232, 308, 311, 313 ], [ 16, 44, 51, 56, 191, 242, 265, 278, 288, 293 ], [ 2, 12, 27, 95, 176, 198, 234, 309, 310, 315 ], [ 1, 13, 26, 94, 189, 240, 267, 276, 290, 295 ], [ 13, 41, 53, 54, 174, 200, 236, 307, 312, 317 ], [ 12, 40, 52, 55, 187, 238, 269, 274, 292, 297 ], [ 5, 16, 23, 91, 172, 202, 238, 305, 314, 319 ], [ 0, 17, 22, 90, 185, 236, 271, 272, 294, 299 ], [ 9, 37, 49, 58, 170, 204, 240, 303, 316, 321 ], [ 8, 36, 48, 59, 183, 234, 270, 273, 296, 301 ], [ 8, 19, 20, 87, 168, 206, 242, 301, 318, 323 ], [ 9, 18, 21, 86, 181, 232, 268, 275, 298, 303 ], [ 0, 33, 45, 62, 167, 208, 244, 299, 320, 322 ], [ 5, 32, 44, 63, 179, 230, 266, 277, 300, 305 ], [ 12, 15, 24, 83, 165, 210, 246, 297, 320, 322 ], [ 13, 14, 25, 82, 177, 228, 264, 279, 302, 307 ], [ 1, 29, 41, 66, 164, 212, 248, 295, 318, 323 ], [ 2, 28, 40, 67, 175, 226, 262, 281, 304, 309 ], [ 11, 16, 28, 79, 163, 214, 250, 293, 316, 321 ], [ 10, 17, 29, 78, 173, 224, 260, 283, 306, 311 ], [ 3, 25, 37, 70, 166, 216, 252, 291, 314, 319 ], [ 4, 24, 36, 71, 171, 222, 258, 285, 308, 313 ], [ 7, 20, 32, 75, 162, 218, 254, 289, 312, 317 ], [ 6, 21, 33, 74, 169, 220, 256, 287, 310, 315 ] ], "Z": [ [ 7, 13, 41, 62, 98, 160, 244, 295, 307, 312 ], [ 9, 11, 37, 66, 102, 156, 248, 291, 303, 316 ], [ 7, 13, 35, 68, 104, 154, 249, 290, 302, 317 ], [ 0, 15, 33, 70, 106, 152, 252, 287, 299, 320 ], [ 9, 11, 39, 64, 100, 158, 253, 286, 298, 321 ], [ 4, 17, 31, 72, 108, 150, 245, 294, 306, 313 ], [ 1, 19, 29, 74, 110, 148, 256, 283, 295, 323 ], [ 0, 15, 43, 60, 96, 161, 257, 282, 294, 322 ], [ 2, 21, 27, 76, 112, 146, 241, 298, 309, 310 ], [ 4, 17, 45, 58, 94, 159, 240, 299, 308, 311 ], [ 3, 23, 25, 78, 114, 144, 260, 279, 291, 319 ], [ 1, 19, 47, 56, 92, 157, 261, 278, 290, 318 ], [ 5, 23, 25, 80, 116, 142, 237, 302, 305, 314 ], [ 2, 21, 49, 54, 90, 155, 236, 303, 304, 315 ], [ 6, 21, 27, 82, 118, 140, 264, 275, 287, 315 ], [ 3, 23, 51, 52, 88, 153, 265, 274, 286, 314 ], [ 8, 19, 29, 84, 120, 138, 233, 301, 306, 318 ], [ 5, 25, 50, 53, 86, 151, 232, 300, 307, 319 ], [ 10, 17, 31, 86, 122, 136, 268, 271, 283, 311 ], [ 6, 27, 48, 55, 84, 149, 269, 270, 282, 310 ], [ 12, 15, 33, 88, 124, 134, 229, 297, 310, 322 ], [ 8, 29, 46, 57, 82, 147, 228, 296, 311, 323 ], [ 13, 14, 35, 90, 126, 132, 267, 272, 279, 307 ], [ 10, 31, 44, 59, 80, 145, 266, 273, 278, 306 ], [ 11, 16, 37, 92, 128, 130, 225, 293, 314, 321 ], [ 12, 33, 42, 61, 78, 143, 224, 292, 315, 320 ], [ 9, 18, 39, 94, 128, 130, 263, 275, 276, 303 ], [ 14, 35, 40, 63, 76, 141, 262, 274, 277, 302 ], [ 7, 20, 41, 96, 126, 132, 221, 289, 317, 318 ], [ 16, 37, 38, 65, 74, 139, 220, 288, 316, 319 ], [ 0, 22, 43, 98, 124, 134, 259, 271, 280, 299 ], [ 18, 36, 39, 67, 72, 137, 258, 270, 281, 298 ], [ 4, 24, 45, 100, 122, 136, 217, 285, 313, 322 ], [ 20, 34, 41, 69, 70, 135, 216, 284, 312, 323 ], [ 1, 26, 47, 102, 120, 138, 255, 267, 284, 295 ], [ 22, 32, 43, 68, 71, 133, 254, 266, 285, 294 ], [ 2, 28, 49, 104, 118, 140, 213, 281, 309, 321 ], [ 24, 30, 45, 66, 73, 131, 212, 280, 308, 320 ], [ 3, 30, 51, 106, 116, 142, 251, 263, 288, 291 ], [ 26, 28, 47, 64, 75, 129, 250, 262, 289, 290 ], [ 5, 32, 53, 108, 114, 144, 209, 277, 305, 317 ], [ 26, 28, 49, 62, 77, 127, 208, 276, 304, 316 ], [ 6, 34, 55, 110, 112, 146, 247, 259, 287, 292 ], [ 24, 30, 51, 60, 79, 125, 246, 258, 286, 293 ], [ 8, 36, 57, 110, 112, 148, 205, 273, 301, 313 ], [ 22, 32, 53, 58, 81, 123, 204, 272, 300, 312 ], [ 10, 38, 59, 108, 114, 150, 243, 255, 283, 296 ], [ 20, 34, 55, 56, 83, 121, 242, 254, 282, 297 ], [ 12, 40, 61, 106, 116, 152, 201, 269, 297, 309 ], [ 18, 36, 54, 57, 85, 119, 200, 268, 296, 308 ], [ 14, 42, 63, 104, 118, 154, 239, 251, 279, 300 ], [ 16, 38, 52, 59, 87, 117, 238, 250, 278, 301 ], [ 16, 44, 65, 102, 120, 156, 197, 265, 293, 305 ], [ 14, 40, 50, 61, 89, 115, 196, 264, 292, 304 ], [ 18, 46, 67, 100, 122, 158, 235, 247, 275, 304 ], [ 12, 42, 48, 63, 91, 113, 234, 246, 274, 305 ], [ 20, 48, 69, 98, 124, 160, 193, 261, 289, 301 ], [ 10, 44, 46, 65, 93, 111, 192, 260, 288, 300 ], [ 22, 50, 71, 96, 126, 161, 231, 243, 271, 308 ], [ 8, 44, 46, 67, 95, 109, 230, 242, 270, 309 ], [ 24, 52, 73, 94, 128, 159, 189, 257, 285, 297 ], [ 6, 42, 48, 69, 97, 107, 188, 256, 284, 296 ], [ 26, 54, 75, 92, 130, 157, 227, 239, 267, 312 ], [ 5, 40, 50, 71, 99, 105, 226, 238, 266, 313 ], [ 28, 56, 77, 90, 132, 155, 185, 253, 281, 293 ], [ 3, 38, 52, 73, 101, 103, 184, 252, 280, 292 ], [ 30, 58, 79, 88, 134, 153, 223, 235, 263, 316 ], [ 2, 36, 54, 75, 101, 103, 222, 234, 262, 317 ], [ 32, 60, 81, 86, 136, 151, 181, 249, 277, 289 ], [ 1, 34, 56, 77, 99, 105, 180, 248, 276, 288 ], [ 34, 62, 83, 84, 138, 149, 219, 231, 259, 320 ], [ 4, 32, 58, 79, 97, 107, 218, 230, 258, 321 ], [ 36, 64, 82, 85, 140, 147, 177, 245, 273, 285 ], [ 0, 30, 60, 81, 95, 109, 176, 244, 272, 284 ], [ 38, 66, 80, 87, 142, 145, 215, 227, 255, 323 ], [ 7, 28, 62, 83, 93, 111, 214, 226, 254, 322 ], [ 40, 68, 78, 89, 143, 144, 173, 241, 269, 281 ], [ 9, 26, 64, 85, 91, 113, 172, 240, 268, 280 ], [ 42, 70, 76, 91, 141, 146, 211, 223, 251, 319 ], [ 11, 24, 66, 87, 89, 115, 210, 222, 250, 318 ], [ 44, 72, 74, 93, 139, 148, 169, 237, 265, 277 ], [ 13, 22, 68, 87, 89, 117, 168, 236, 264, 276 ], [ 46, 72, 74, 95, 137, 150, 207, 219, 247, 315 ], [ 15, 20, 70, 85, 91, 119, 206, 218, 246, 314 ], [ 48, 70, 76, 97, 135, 152, 166, 233, 261, 273 ], [ 17, 18, 72, 83, 93, 121, 165, 232, 260, 272 ], [ 50, 68, 78, 99, 133, 154, 203, 215, 243, 311 ], [ 16, 19, 74, 81, 95, 123, 202, 214, 242, 310 ], [ 52, 66, 80, 101, 131, 156, 164, 229, 257, 269 ], [ 14, 21, 76, 79, 97, 125, 163, 228, 256, 268 ], [ 54, 64, 82, 103, 129, 158, 199, 211, 239, 307 ], [ 12, 23, 77, 78, 99, 127, 198, 210, 238, 306 ], [ 56, 62, 84, 105, 127, 160, 167, 225, 253, 265 ], [ 10, 25, 75, 80, 101, 129, 162, 224, 252, 264 ], [ 58, 60, 86, 107, 125, 161, 195, 207, 235, 303 ], [ 8, 27, 73, 82, 103, 131, 194, 206, 234, 302 ], [ 58, 60, 88, 109, 123, 159, 170, 221, 249, 261 ], [ 6, 29, 71, 84, 105, 133, 171, 220, 248, 260 ], [ 56, 62, 90, 111, 121, 157, 191, 203, 231, 299 ], [ 5, 31, 69, 86, 107, 135, 190, 202, 230, 298 ], [ 54, 64, 92, 113, 119, 155, 174, 217, 245, 257 ], [ 3, 33, 67, 88, 109, 137, 175, 216, 244, 256 ], [ 52, 66, 94, 115, 117, 153, 187, 199, 227, 295 ], [ 2, 35, 65, 90, 111, 139, 186, 198, 226, 294 ], [ 50, 68, 96, 115, 117, 151, 178, 213, 241, 253 ], [ 1, 37, 63, 92, 113, 141, 179, 212, 240, 252 ], [ 48, 70, 98, 113, 119, 149, 183, 195, 223, 291 ], [ 4, 39, 61, 94, 115, 143, 182, 194, 222, 290 ], [ 46, 72, 100, 111, 121, 147, 182, 209, 237, 249 ], [ 0, 41, 59, 96, 117, 145, 183, 208, 236, 248 ], [ 44, 74, 102, 109, 123, 145, 179, 191, 219, 287 ], [ 7, 43, 57, 98, 119, 147, 178, 190, 218, 286 ], [ 42, 76, 104, 107, 125, 143, 186, 205, 233, 245 ], [ 9, 45, 55, 100, 121, 149, 187, 204, 232, 244 ], [ 40, 78, 105, 106, 127, 141, 175, 187, 215, 283 ], [ 11, 47, 53, 102, 123, 151, 174, 186, 214, 282 ], [ 38, 80, 103, 108, 129, 139, 190, 201, 229, 241 ], [ 13, 49, 51, 104, 125, 153, 191, 200, 228, 240 ], [ 36, 82, 101, 110, 131, 137, 171, 183, 211, 279 ], [ 15, 49, 51, 106, 127, 155, 170, 182, 210, 278 ], [ 34, 84, 99, 112, 133, 135, 194, 197, 225, 237 ], [ 17, 47, 53, 108, 129, 157, 195, 196, 224, 236 ], [ 32, 86, 97, 114, 133, 135, 162, 179, 207, 275 ], [ 19, 45, 55, 110, 131, 159, 167, 178, 206, 274 ], [ 30, 88, 95, 116, 131, 137, 193, 198, 221, 233 ], [ 21, 43, 57, 112, 133, 161, 192, 199, 220, 232 ], [ 28, 90, 93, 118, 129, 139, 163, 175, 203, 271 ], [ 23, 41, 59, 114, 135, 160, 164, 174, 202, 270 ], [ 26, 91, 92, 120, 127, 141, 189, 202, 217, 229 ], [ 25, 39, 61, 116, 137, 158, 188, 203, 216, 228 ], [ 24, 89, 94, 122, 125, 143, 165, 171, 199, 267 ], [ 27, 37, 63, 118, 139, 156, 166, 170, 198, 266 ], [ 22, 87, 96, 123, 124, 145, 185, 206, 213, 225 ], [ 29, 35, 65, 120, 141, 154, 184, 207, 212, 224 ], [ 20, 85, 98, 121, 126, 147, 162, 168, 195, 263 ], [ 31, 33, 67, 122, 143, 152, 167, 169, 194, 262 ], [ 18, 83, 100, 119, 128, 149, 181, 209, 210, 221 ], [ 31, 33, 69, 124, 145, 150, 180, 208, 211, 220 ], [ 16, 81, 102, 117, 130, 151, 163, 172, 191, 259 ], [ 29, 35, 71, 126, 147, 148, 164, 173, 190, 258 ], [ 14, 79, 104, 115, 132, 153, 177, 205, 214, 217 ], [ 27, 37, 73, 128, 146, 149, 176, 204, 215, 216 ], [ 12, 77, 106, 113, 134, 155, 165, 176, 187, 255 ], [ 25, 39, 75, 130, 144, 151, 166, 177, 186, 254 ], [ 10, 75, 108, 111, 136, 157, 173, 201, 213, 218 ], [ 23, 41, 77, 132, 142, 153, 172, 200, 212, 219 ], [ 8, 73, 109, 110, 138, 159, 168, 180, 183, 251 ], [ 21, 43, 79, 134, 140, 155, 169, 181, 182, 250 ], [ 6, 71, 107, 112, 140, 161, 169, 197, 209, 222 ], [ 19, 45, 81, 136, 138, 157, 168, 196, 208, 223 ], [ 5, 69, 105, 114, 142, 160, 172, 179, 184, 247 ], [ 17, 47, 83, 136, 138, 159, 173, 178, 185, 246 ], [ 3, 67, 103, 116, 144, 158, 166, 193, 205, 226 ], [ 15, 49, 85, 134, 140, 161, 165, 192, 204, 227 ], [ 2, 65, 101, 118, 146, 156, 175, 176, 188, 243 ], [ 13, 51, 87, 132, 142, 160, 174, 177, 189, 242 ], [ 1, 63, 99, 120, 148, 154, 164, 189, 201, 230 ], [ 11, 53, 89, 130, 144, 158, 163, 188, 200, 231 ], [ 4, 61, 97, 122, 150, 152, 171, 180, 192, 239 ], [ 9, 55, 91, 128, 146, 156, 170, 181, 193, 238 ], [ 0, 59, 95, 124, 150, 152, 167, 185, 197, 234 ], [ 7, 57, 93, 126, 148, 154, 162, 184, 196, 235 ] ] }, "distance": { "d": 30, "X": { "value": 30, "confidence": "upper_bound", "witness": [ 12, 22, 85, 95, 120, 130, 162, 163, 165, 166, 184, 185, 189, 193, 238, 242, 246, 247, 264, 266, 267, 268, 271, 272, 273, 275, 292, 293, 297, 301 ] }, "Z": { "value": 30, "confidence": "upper_bound", "witness": [ 1, 3, 11, 15, 25, 39, 40, 53, 54, 67, 68, 82, 92, 96, 105, 106, 109, 110, 119, 123, 133, 147, 148, 161, 187, 214, 217, 244, 295, 322 ] } }, "family": "lifted-product", "provenance": { "authors": [ "@vprusso" ], "construction": "Two-block group algebra code over the dihedral group D81 (order 162): HX = [L[a] L[b]], HZ = [R[b] R[a]] with element-index supports a=[82, 133, 145, 150], b=[7, 13, 41, 62, 98, 160] in the left/right regular representation; n = 2|G|, max check weight 10.", "references": [], "date": "2026-08-06", "notes": "Found by a MAP-Elites search over non-abelian 2BGA codes gated by an escalating distance ladder; the reported d is the minimum over multi-seed randomized information-set searches at 200k, 2M and 20M iterations (values agreed across all rungs), with the recorded per-side witnesses extracted at the 20M budget.", "model": "Claude Opus 5" } }