Best Known (70−54, 70, s)-Nets in Base 25
(70−54, 70, 126)-Net over F25 — Constructive and digital
Digital (16, 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
(70−54, 70, 150)-Net over F25 — Digital
Digital (16, 70, 150)-net over F25, using
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
(70−54, 70, 1902)-Net in Base 25 — Upper bound on s
There is no (16, 70, 1903)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 72 466486 575128 900087 949294 595153 815502 318080 345354 729839 477664 335366 162913 604634 807488 877916 659449 > 2570 [i]