Best Known (12, 12+27, s)-Nets in Base 25
(12, 12+27, 126)-Net over F25 — Constructive and digital
Digital (12, 39, 126)-net over F25, using
- t-expansion [i] based on digital (10, 39, 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
(12, 12+27, 2874)-Net in Base 25 — Upper bound on s
There is no (12, 39, 2875)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 38, 2875)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 132917 607917 300309 888131 190623 323467 350973 091109 012201 > 2538 [i]