Best Known (101−61, 101, s)-Nets in Base 7
(101−61, 101, 41)-Net over F7 — Constructive and digital
Digital (40, 101, 41)-net over F7, using
- net from sequence [i] based on digital (40, 40)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 40)-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, 40)-sequence over F49, using
(101−61, 101, 96)-Net over F7 — Digital
Digital (40, 101, 96)-net over F7, using
- t-expansion [i] based on digital (33, 101, 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
(101−61, 101, 1297)-Net in Base 7 — Upper bound on s
There is no (40, 101, 1298)-net in base 7, because
- 1 times m-reduction [i] would yield (40, 100, 1298)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 3 254512 480497 823097 227370 901944 404315 328784 941971 655367 337379 259957 760644 953604 429853 > 7100 [i]