Best Known (38, 38+61, s)-Nets in Base 7
(38, 38+61, 39)-Net over F7 — Constructive and digital
Digital (38, 99, 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
(38, 38+61, 96)-Net over F7 — Digital
Digital (38, 99, 96)-net over F7, using
- t-expansion [i] based on digital (33, 99, 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
(38, 38+61, 1137)-Net in Base 7 — Upper bound on s
There is no (38, 99, 1138)-net in base 7, because
- 1 times m-reduction [i] would yield (38, 98, 1138)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 66885 071711 297494 048958 807344 282077 287584 061747 053345 717106 625894 305315 178426 430813 > 798 [i]