Best Known (9, 45, s)-Nets in Base 7
(9, 45, 17)-Net over F7 — Constructive and digital
Digital (9, 45, 17)-net over F7, using
- net from sequence [i] based on digital (9, 16)-sequence over F7, using
(9, 45, 38)-Net over F7 — Digital
Digital (9, 45, 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
(9, 45, 144)-Net in Base 7 — Upper bound on s
There is no (9, 45, 145)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(745, 145, S7, 36), but
- the linear programming bound shows that M ≥ 1 813054 297468 894563 118987 208872 174502 813939 418289 052616 398499 773838 510369 693534 865836 965625 / 16446 905309 677963 308897 231434 343903 438067 922584 484783 > 745 [i]