Best Known (57−53, 57, s)-Nets in Base 25
(57−53, 57, 66)-Net over F25 — Constructive and digital
Digital (4, 57, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
(57−53, 57, 387)-Net in Base 25 — Upper bound on s
There is no (4, 57, 388)-net in base 25, because
- 21 times m-reduction [i] would yield (4, 36, 388)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 212 867301 584337 671224 184862 902302 351269 285411 623425 > 2536 [i]