Best Known (78−43, 78, s)-Nets in Base 7
(78−43, 78, 36)-Net over F7 — Constructive and digital
Digital (35, 78, 36)-net over F7, using
- net from sequence [i] based on digital (35, 35)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 35)-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
- Niederreiter sequence [i]
- base reduction for sequences [i] based on digital (0, 35)-sequence over F49, using
(78−43, 78, 96)-Net over F7 — Digital
Digital (35, 78, 96)-net over F7, using
- t-expansion [i] based on digital (33, 78, 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
(78−43, 78, 1802)-Net in Base 7 — Upper bound on s
There is no (35, 78, 1803)-net in base 7, because
- 1 times m-reduction [i] would yield (35, 77, 1803)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 119292 399665 428945 167278 418337 063378 169280 531348 542153 953625 062219 > 777 [i]