MinT - Best Known (58−35, 58, s)-Nets in Base 25

Best Known (58−35, 58, s)-Nets in Base 25

(58−35, 58, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 58, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 58, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(58−35, 58, 176)-Net over F₂₅ — Digital

Digital (23, 58, 176)-net over F₂₅, using

net from sequence [i] based on digital (23, 175)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 23 and N(F) ≥ 176, using
  - an algebraic function field by Teo [i]

(58−35, 58, 14544)-Net in Base 25 — Upper bound on s

There is no (23, 58, 14545)-net in base 25, because

1 times m-reduction [i] would yield (23, 57, 14545)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 48 203026 920987 684488 457981 910078 836231 285845 330864 791482 131693 489226 480347 668249 > 25⁵⁷ [i]