Best Known (91−51, 91, s)-Nets in Base 7
(91−51, 91, 41)-Net over F7 — Constructive and digital
Digital (40, 91, 41)-net over F7, using
- net from sequence [i] based on digital (40, 40)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 40)-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, 40)-sequence over F49, using
(91−51, 91, 96)-Net over F7 — Digital
Digital (40, 91, 96)-net over F7, using
- t-expansion [i] based on digital (33, 91, 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
(91−51, 91, 1853)-Net in Base 7 — Upper bound on s
There is no (40, 91, 1854)-net in base 7, because
- 1 times m-reduction [i] would yield (40, 90, 1854)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 11478 431778 493675 183152 405759 960120 888293 594621 828590 407393 273836 204693 634181 > 790 [i]