Best Known (51−38, 51, s)-Nets in Base 25
(51−38, 51, 126)-Net over F25 — Constructive and digital
Digital (13, 51, 126)-net over F25, using
- t-expansion [i] based on digital (10, 51, 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
(51−38, 51, 1858)-Net in Base 25 — Upper bound on s
There is no (13, 51, 1859)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 198848 783642 557094 265367 349524 921349 773379 900623 457904 341843 627729 188825 > 2551 [i]