Best Known (58−45, 58, s)-Nets in Base 25
(58−45, 58, 126)-Net over F25 — Constructive and digital
Digital (13, 58, 126)-net over F25, using
- t-expansion [i] based on digital (10, 58, 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
(58−45, 58, 1568)-Net in Base 25 — Upper bound on s
There is no (13, 58, 1569)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 57, 1569)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 48 611697 055239 646073 174678 649997 418538 290877 501397 254242 973973 944232 630322 030545 > 2557 [i]