Best Known (45, 45+59, s)-Nets in Base 7
(45, 45+59, 46)-Net over F7 — Constructive and digital
Digital (45, 104, 46)-net over F7, using
- net from sequence [i] based on digital (45, 45)-sequence over F7, using
- base reduction for sequences [i] based on digital (0, 45)-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, 45)-sequence over F49, using
(45, 45+59, 105)-Net over F7 — Digital
Digital (45, 104, 105)-net over F7, using
- t-expansion [i] based on digital (43, 104, 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
(45, 45+59, 1933)-Net in Base 7 — Upper bound on s
There is no (45, 104, 1934)-net in base 7, because
- 1 times m-reduction [i] would yield (45, 103, 1934)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 1118 826926 698867 977882 826706 695358 842528 692805 701128 083442 484390 492396 963253 199585 419933 > 7103 [i]