Best Known (45, 45+58, s)-Nets in Base 5
(45, 45+58, 78)-Net over F5 — Constructive and digital
Digital (45, 103, 78)-net over F5, using
- t-expansion [i] based on digital (38, 103, 78)-net over F5, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
(45, 45+58, 88)-Net over F5 — Digital
Digital (45, 103, 88)-net over F5, using
- net from sequence [i] based on digital (45, 87)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 45 and N(F) ≥ 88, using
(45, 45+58, 865)-Net in Base 5 — Upper bound on s
There is no (45, 103, 866)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 009194 299937 654713 209122 434986 055435 189812 709496 324684 779012 064351 299465 > 5103 [i]