Best Known (44, 105, s)-Nets in Base 7
(44, 105, 45)-Net over F7 — Constructive and digital
Digital (44, 105, 45)-net over F7, using
- net from sequence [i] based on digital (44, 44)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 44)-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, 44)-sequence over F49, using
(44, 105, 105)-Net over F7 — Digital
Digital (44, 105, 105)-net over F7, using
- t-expansion [i] based on digital (43, 105, 105)-net over F7, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
- net from sequence [i] based on digital (43, 104)-sequence over F7, using
(44, 105, 1687)-Net in Base 7 — Upper bound on s
There is no (44, 105, 1688)-net in base 7, because
- 1 times m-reduction [i] would yield (44, 104, 1688)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 7783 163060 977141 222055 396573 662832 803445 794197 893600 013524 264712 167686 305611 370098 078161 > 7104 [i]