Best Known (87−49, 87, s)-Nets in Base 7
(87−49, 87, 39)-Net over F7 — Constructive and digital
Digital (38, 87, 39)-net over F7, using
- net from sequence [i] based on digital (38, 38)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 38)-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, 38)-sequence over F49, using
(87−49, 87, 96)-Net over F7 — Digital
Digital (38, 87, 96)-net over F7, using
- t-expansion [i] based on digital (33, 87, 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
(87−49, 87, 1728)-Net in Base 7 — Upper bound on s
There is no (38, 87, 1729)-net in base 7, because
- 1 times m-reduction [i] would yield (38, 86, 1729)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 4 816847 098444 135739 608344 504373 918152 256859 286379 604124 152646 602674 076737 > 786 [i]