Best Known (50−31, 50, s)-Nets in Base 25
(50−31, 50, 148)-Net over F25 — Constructive and digital
Digital (19, 50, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
(50−31, 50, 162)-Net over F25 — Digital
Digital (19, 50, 162)-net over F25, using
- net from sequence [i] based on digital (19, 161)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 162, using
(50−31, 50, 9858)-Net in Base 25 — Upper bound on s
There is no (19, 50, 9859)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 49, 9859)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 315 643913 985036 063074 173308 308377 597571 615573 082575 877687 980476 847545 > 2549 [i]