Best Known (12, s)-Sequences in Base 8
(12, 47)-Sequence over F8 — Constructive and digital
Digital (12, 47)-sequence over F8, using
- t-expansion [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
(12, 48)-Sequence over F8 — Digital
Digital (12, 48)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 12 and N(F) ≥ 49, using
(12, 101)-Sequence in Base 8 — Upper bound on s
There is no (12, 102)-sequence in base 8, because
- net from sequence [i] would yield (12, m, 103)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (12, 90, 103)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(890, 103, S8, 78), but
- the linear programming bound shows that M ≥ 1021 576153 078735 923643 496828 494105 918576 721926 818258 715769 540997 787100 910918 672673 951195 332608 / 431023 326525 > 890 [i]
- extracting embedded orthogonal array [i] would yield OA(890, 103, S8, 78), but
- m-reduction [i] would yield (12, 90, 103)-net in base 8, but