Best Known (12, 74, s)-Nets in Base 7
(12, 74, 20)-Net over F7 — Constructive and digital
Digital (12, 74, 20)-net over F7, using
- net from sequence [i] based on digital (12, 19)-sequence over F7, using
(12, 74, 38)-Net over F7 — Digital
Digital (12, 74, 38)-net over F7, using
- t-expansion [i] based on digital (9, 74, 38)-net over F7, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
(12, 74, 111)-Net in Base 7 — Upper bound on s
There is no (12, 74, 112)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(774, 112, S7, 62), but
- the linear programming bound shows that M ≥ 323 023705 901868 326618 060630 697417 174001 339767 969424 900292 735271 338809 195763 088795 682895 480156 241591 788493 327335 / 906890 224630 673356 794926 540051 067157 304375 029584 > 774 [i]