Best Known (12, 12+59, s)-Nets in Base 25
(12, 12+59, 126)-Net over F25 — Constructive and digital
Digital (12, 71, 126)-net over F25, using
- t-expansion [i] based on digital (10, 71, 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+59, 1136)-Net in Base 25 — Upper bound on s
There is no (12, 71, 1137)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 70, 1137)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 73 027879 992807 444849 334659 900077 540653 263123 652198 497572 616390 894248 763179 238909 038410 004191 524025 > 2570 [i]