Best Known (108−63, 108, s)-Nets in Base 7
(108−63, 108, 46)-Net over F7 — Constructive and digital
Digital (45, 108, 46)-net over F7, using
- net from sequence [i] based on digital (45, 45)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 45)-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, 45)-sequence over F49, using
(108−63, 108, 105)-Net over F7 — Digital
Digital (45, 108, 105)-net over F7, using
- t-expansion [i] based on digital (43, 108, 105)-net over F7, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
(108−63, 108, 1689)-Net in Base 7 — Upper bound on s
There is no (45, 108, 1690)-net in base 7, because
- 1 times m-reduction [i] would yield (45, 107, 1690)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 2 699362 840062 686289 016268 494283 000254 266554 181256 531519 061172 206962 682688 537551 115069 990481 > 7107 [i]