Best Known (57−45, 57, s)-Nets in Base 25
(57−45, 57, 126)-Net over F25 — Constructive and digital
Digital (12, 57, 126)-net over F25, using
- t-expansion [i] based on digital (10, 57, 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
(57−45, 57, 1353)-Net in Base 25 — Upper bound on s
There is no (12, 57, 1354)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 56, 1354)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1 947874 023862 556728 673566 470578 257982 400855 621500 754902 231322 966417 783557 225185 > 2556 [i]