Best Known (37, 37+73, s)-Nets in Base 7
(37, 37+73, 38)-Net over F7 — Constructive and digital
Digital (37, 110, 38)-net over F7, using
- net from sequence [i] based on digital (37, 37)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 37)-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, 37)-sequence over F49, using
(37, 37+73, 96)-Net over F7 — Digital
Digital (37, 110, 96)-net over F7, using
- t-expansion [i] based on digital (33, 110, 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
(37, 37+73, 838)-Net in Base 7 — Upper bound on s
There is no (37, 110, 839)-net in base 7, because
- 1 times m-reduction [i] would yield (37, 109, 839)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 133 835630 233658 433269 011538 442364 353001 376715 470116 918114 283385 992988 468247 044599 837248 938025 > 7109 [i]