MinT - Best Known (96−74, 96, s)-Nets in Base 25

Best Known (96−74, 96, s)-Nets in Base 25

(96−74, 96, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 96, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 96, 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]

(96−74, 96, 171)-Net over F₂₅ — Digital

Digital (22, 96, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 96, 171)-net over F₂₅, using
- net from sequence [i] based on digital (20, 170)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 20 and N(F) ≥ 171, using
    - an algebraic function field by Teo [i]

(96−74, 96, 2567)-Net in Base 25 — Upper bound on s

There is no (22, 96, 2568)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 160 585100 257258 763406 012493 859231 721741 372629 645398 780569 788295 006042 846299 739592 147084 658019 020553 216336 906337 128174 342118 118150 129089 > 25⁹⁶ [i]