Home.

Recall the original basis U = { U0, U1, U2, U3, U4, U5, U6, U7 }. From a symbol ♦wxyz in the table below, select the indicated members of U and construct the subspace whose basis is U′ = { Uw, Ux, Uy, Uz }.

Each diamond quadruple indicates a subspace U′ in which a 3-in-8 is a closed operation, and this applies to any 3-in-8 that is based on that permutation. Each permutation is shared by precisely thirty-two 3-in-8s, which differ in the distribution of positive and negative signs.

 permutationdesignator p01 ♦0123 ♦0145 ♦0167 ♦0246 ♦0257 ♦0347 ♦0356 ♦1247 ♦1256 ♦1346 ♦1357 ♦2345 ♦2367 ♦4567 p02 ♦0123 ♦0145 ♦0167 ♦0247 ♦0256 ♦0346 ♦0357 ♦1246 ♦1257 ♦1347 ♦1356 ♦2345 ♦2367 ♦4567 p03 ♦0123 ♦0146 ♦0157 ♦0245 ♦0267 ♦0347 ♦0356 ♦1247 ♦1256 ♦1345 ♦1367 ♦2346 ♦2357 ♦4567 p04 ♦0123 ♦0146 ♦0157 ♦0247 ♦0256 ♦0345 ♦0367 ♦1245 ♦1267 ♦1347 ♦1356 ♦2346 ♦2357 ♦4567 p05 ♦0123 ♦0147 ♦0156 ♦0246 ♦0257 ♦0345 ♦0367 ♦1245 ♦1267 ♦1346 ♦1357 ♦2347 ♦2356 ♦4567 p06 ♦0123 ♦0147 ♦0156 ♦0245 ♦0267 ♦0346 ♦0357 ♦1246 ♦1257 ♦1345 ♦1367 ♦2347 ♦2356 ♦4567 p07 ♦0124 ♦0135 ♦0167 ♦0236 ♦0257 ♦0347 ♦0456 ♦1237 ♦1256 ♦1346 ♦1457 ♦2345 ♦2467 ♦3567 p08 ♦0124 ♦0135 ♦0167 ♦0237 ♦0256 ♦0346 ♦0457 ♦1236 ♦1257 ♦1347 ♦1456 ♦2345 ♦2467 ♦3567 p09 ♦0124 ♦0136 ♦0157 ♦0235 ♦0267 ♦0347 ♦0456 ♦1237 ♦1256 ♦1345 ♦1467 ♦2346 ♦2457 ♦3567 p10 ♦0124 ♦0136 ♦0157 ♦0237 ♦0256 ♦0345 ♦0467 ♦1235 ♦1267 ♦1347 ♦1456 ♦2346 ♦2457 ♦3567 p11 ♦0124 ♦0137 ♦0156 ♦0236 ♦0257 ♦0345 ♦0467 ♦1235 ♦1267 ♦1346 ♦1457 ♦2347 ♦2456 ♦3567 p12 ♦0124 ♦0137 ♦0156 ♦0235 ♦0267 ♦0346 ♦0457 ♦1236 ♦1257 ♦1345 ♦1467 ♦2347 ♦2456 ♦3567 p13 ♦0125 ♦0134 ♦0167 ♦0237 ♦0246 ♦0356 ♦0457 ♦1236 ♦1247 ♦1357 ♦1456 ♦2345 ♦2567 ♦3467 p14 ♦0125 ♦0134 ♦0167 ♦0236 ♦0247 ♦0357 ♦0456 ♦1237 ♦1246 ♦1356 ♦1457 ♦2345 ♦2567 ♦3467 p15 ♦0125 ♦0137 ♦0146 ♦0234 ♦0267 ♦0356 ♦0457 ♦1236 ♦1247 ♦1345 ♦1567 ♦2357 ♦2456 ♦3467 p16 ♦0125 ♦0137 ♦0146 ♦0236 ♦0247 ♦0345 ♦0567 ♦1234 ♦1267 ♦1356 ♦1457 ♦2357 ♦2456 ♦3467 p17 ♦0125 ♦0136 ♦0147 ♦0237 ♦0246 ♦0345 ♦0567 ♦1234 ♦1267 ♦1357 ♦1456 ♦2356 ♦2457 ♦3467 p18 ♦0125 ♦0136 ♦0147 ♦0234 ♦0267 ♦0357 ♦0456 ♦1237 ♦1246 ♦1345 ♦1567 ♦2356 ♦2457 ♦3467 p19 ♦0126 ♦0137 ♦0145 ♦0234 ♦0257 ♦0356 ♦0467 ♦1235 ♦1247 ♦1346 ♦1567 ♦2367 ♦2456 ♦3457 p20 ♦0126 ♦0137 ♦0145 ♦0235 ♦0247 ♦0346 ♦0567 ♦1234 ♦1257 ♦1356 ♦1467 ♦2367 ♦2456 ♦3457 p21 ♦0126 ♦0134 ♦0157 ♦0237 ♦0245 ♦0356 ♦0467 ♦1235 ♦1247 ♦1367 ♦1456 ♦2346 ♦2567 ♦3457 p22 ♦0126 ♦0134 ♦0157 ♦0235 ♦0247 ♦0367 ♦0456 ♦1237 ♦1245 ♦1356 ♦1467 ♦2346 ♦2567 ♦3457 p23 ♦0126 ♦0135 ♦0147 ♦0234 ♦0257 ♦0367 ♦0456 ♦1237 ♦1245 ♦1346 ♦1567 ♦2356 ♦2467 ♦3457 p24 ♦0126 ♦0135 ♦0147 ♦0237 ♦0245 ♦0346 ♦0567 ♦1234 ♦1257 ♦1367 ♦1456 ♦2356 ♦2467 ♦3457 p25 ♦0127 ♦0136 ♦0145 ♦0235 ♦0246 ♦0347 ♦0567 ♦1234 ♦1256 ♦1357 ♦1467 ♦2367 ♦2457 ♦3456 p26 ♦0127 ♦0136 ♦0145 ♦0234 ♦0256 ♦0357 ♦0467 ♦1235 ♦1246 ♦1347 ♦1567 ♦2367 ♦2457 ♦3456 p27 ♦0127 ♦0135 ♦0146 ♦0236 ♦0245 ♦0347 ♦0567 ♦1234 ♦1256 ♦1367 ♦1457 ♦2357 ♦2467 ♦3456 p28 ♦0127 ♦0135 ♦0146 ♦0234 ♦0256 ♦0367 ♦0457 ♦1236 ♦1245 ♦1347 ♦1567 ♦2357 ♦2467 ♦3456 p29 ♦0127 ♦0134 ♦0156 ♦0235 ♦0246 ♦0367 ♦0457 ♦1236 ♦1245 ♦1357 ♦1467 ♦2347 ♦2567 ♦3456 p30 ♦0127 ♦0134 ♦0156 ♦0236 ♦0245 ♦0357 ♦0467 ♦1235 ♦1246 ♦1367 ♦1457 ♦2347 ♦2567 ♦3456