Best Known (64−48, 64, s)-Nets in Base 25
(64−48, 64, 126)-Net over F25 — Constructive and digital
Digital (16, 64, 126)-net over F25, using
- t-expansion [i] based on digital (10, 64, 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
(64−48, 64, 150)-Net over F25 — Digital
Digital (16, 64, 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
(64−48, 64, 2170)-Net in Base 25 — Upper bound on s
There is no (16, 64, 2171)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 296457 449928 111763 900677 211622 354864 707742 936207 255788 625586 569072 449172 087217 756420 921025 > 2564 [i]