Best Known (107−67, 107, s)-Nets in Base 7
(107−67, 107, 41)-Net over F7 — Constructive and digital
Digital (40, 107, 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
(107−67, 107, 96)-Net over F7 — Digital
Digital (40, 107, 96)-net over F7, using
- t-expansion [i] based on digital (33, 107, 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
(107−67, 107, 1115)-Net in Base 7 — Upper bound on s
There is no (40, 107, 1116)-net in base 7, because
- 1 times m-reduction [i] would yield (40, 106, 1116)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 384659 025326 305920 199269 251969 753418 708502 948229 072601 995608 071615 454718 295863 794327 921705 > 7106 [i]