Best Known (45, 70, s)-Nets in Base 5
(45, 70, 252)-Net over F5 — Constructive and digital
Digital (45, 70, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 35, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(45, 70, 280)-Net over F5 — Digital
Digital (45, 70, 280)-net over F5, using
(45, 70, 13807)-Net in Base 5 — Upper bound on s
There is no (45, 70, 13808)-net in base 5, because
- 1 times m-reduction [i] would yield (45, 69, 13808)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1 694957 069220 546496 528659 148438 207865 196578 914305 > 569 [i]