Best Known (12, s)-Sequences in Base 9
(12, 39)-Sequence over F9 — Constructive and digital
Digital (12, 39)-sequence over F9, using
- t-expansion [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
(12, 55)-Sequence over F9 — Digital
Digital (12, 55)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 12 and N(F) ≥ 56, using
(12, 112)-Sequence in Base 9 — Upper bound on s
There is no (12, 113)-sequence in base 9, because
- net from sequence [i] would yield (12, m, 114)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (12, 99, 114)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(999, 114, S9, 87), but
- the linear programming bound shows that M ≥ 183 712452 224151 496359 730756 773016 045194 033482 014231 382801 426138 213217 418543 740185 901581 517780 371424 905718 474237 / 4987 502939 947913 > 999 [i]
- extracting embedded orthogonal array [i] would yield OA(999, 114, S9, 87), but
- m-reduction [i] would yield (12, 99, 114)-net in base 9, but