MinT - Best Known (34−27, 34, s)-Nets in Base 25

Best Known (34−27, 34, s)-Nets in Base 25

(34−27, 34, 66)-Net over F₂₅ — Constructive and digital

Digital (7, 34, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 34, 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]

(34−27, 34, 828)-Net in Base 25 — Upper bound on s

There is no (7, 34, 829)-net in base 25, because

1 times m-reduction [i] would yield (7, 33, 829)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 13613 425623 540833 179618 025525 842143 441198 333145 > 25³³ [i]