Best Known (59−49, 59, s)-Nets in Base 25
(59−49, 59, 126)-Net over F25 — Constructive and digital
Digital (10, 59, 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
(59−49, 59, 963)-Net in Base 25 — Upper bound on s
There is no (10, 59, 964)-net in base 25, because
- 1 times m-reduction [i] would yield (10, 58, 964)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1213 685825 935570 099955 884890 456190 223499 802512 424929 114156 906278 594276 057972 423425 > 2558 [i]