Best Known (12, 12+25, s)-Nets in Base 25
(12, 12+25, 126)-Net over F25 — Constructive and digital
Digital (12, 37, 126)-net over F25, using
- t-expansion [i] based on digital (10, 37, 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+25, 3437)-Net in Base 25 — Upper bound on s
There is no (12, 37, 3438)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 36, 3438)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 212 300870 320303 195601 384116 303706 272205 066069 605441 > 2536 [i]