MinT - Best Known (4, 4+7, s)-Nets in Base 25

Best Known (4, 4+7, s)-Nets in Base 25

(4, 4+7, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 11, 66)-net over F₂₅, using

net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]

(4, 4+7, 3458)-Net in Base 25 — Upper bound on s

There is no (4, 11, 3459)-net in base 25, because

1 times m-reduction [i] would yield (4, 10, 3459)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 95 446012 494169 > 25¹⁰ [i]