Best Known (35, 35+65, s)-Nets in Base 7
(35, 35+65, 36)-Net over F7 — Constructive and digital
Digital (35, 100, 36)-net over F7, using
- net from sequence [i] based on digital (35, 35)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 35)-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
- Niederreiter sequence [i]
- base reduction for sequences [i] based on digital (0, 35)-sequence over F49, using
(35, 35+65, 96)-Net over F7 — Digital
Digital (35, 100, 96)-net over F7, using
- t-expansion [i] based on digital (33, 100, 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
(35, 35+65, 856)-Net in Base 7 — Upper bound on s
There is no (35, 100, 857)-net in base 7, because
- 1 times m-reduction [i] would yield (35, 99, 857)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 464912 870790 999950 434397 764371 266708 687473 217742 442482 296926 853001 630912 298158 720769 > 799 [i]