Best Known (7, 7+71, s)-Nets in Base 25
(7, 7+71, 66)-Net over F25 — Constructive and digital
Digital (7, 78, 66)-net over F25, using
- t-expansion [i] based on digital (4, 78, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
(7, 7+71, 639)-Net in Base 25 — Upper bound on s
There is no (7, 78, 640)-net in base 25, because
- 21 times m-reduction [i] would yield (7, 57, 640)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 48 659566 175148 101512 620834 056263 397453 835362 908184 627649 101778 555400 862409 268225 > 2557 [i]