Best Known (34−31, 34, s)-Nets in Base 25
(34−31, 34, 52)-Net over F25 — Constructive and digital
Digital (3, 34, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
(34−31, 34, 56)-Net over F25 — Digital
Digital (3, 34, 56)-net over F25, using
- net from sequence [i] based on digital (3, 55)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 56, using
(34−31, 34, 302)-Net in Base 25 — Upper bound on s
There is no (3, 34, 303)-net in base 25, because
- 7 times m-reduction [i] would yield (3, 27, 303)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 57 705850 781438 957998 053643 851512 965345 > 2527 [i]