Best Known (93−56, 93, s)-Nets in Base 7
(93−56, 93, 38)-Net over F7 — Constructive and digital
Digital (37, 93, 38)-net over F7, using
- net from sequence [i] based on digital (37, 37)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 37)-sequence over F49, using
- s-reduction based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- s-reduction based on digital (0, 49)-sequence over F49, using
- base reduction for sequences [i] based on digital (0, 37)-sequence over F49, using
(93−56, 93, 96)-Net over F7 — Digital
Digital (37, 93, 96)-net over F7, using
- t-expansion [i] based on digital (33, 93, 96)-net over F7, using
- net from sequence [i] based on digital (33, 95)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 33 and N(F) ≥ 96, using
- net from sequence [i] based on digital (33, 95)-sequence over F7, using
(93−56, 93, 1189)-Net in Base 7 — Upper bound on s
There is no (37, 93, 1190)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 4 006522 126992 974886 694383 139696 940825 743878 014684 446372 959881 405062 431476 601049 > 793 [i]