Best Known (35−23, 35, s)-Nets in Base 25
(35−23, 35, 126)-Net over F25 — Constructive and digital
Digital (12, 35, 126)-net over F25, using
- t-expansion [i] based on digital (10, 35, 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
(35−23, 35, 4277)-Net in Base 25 — Upper bound on s
There is no (12, 35, 4278)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 34, 4278)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 339551 795951 150047 396305 925714 794853 617713 902705 > 2534 [i]