Best Known (70−57, 70, s)-Nets in Base 25
(70−57, 70, 126)-Net over F25 — Constructive and digital
Digital (13, 70, 126)-net over F25, using
- t-expansion [i] based on digital (10, 70, 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
(70−57, 70, 1296)-Net in Base 25 — Upper bound on s
There is no (13, 70, 1297)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 69, 1297)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 2 887258 681751 110418 619719 386836 530613 704443 605448 209296 402481 397305 536917 027817 655905 312629 756705 > 2569 [i]