MinT - Best Known (81−59, 81, s)-Nets in Base 25

Best Known (81−59, 81, s)-Nets in Base 25

(81−59, 81, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 81, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 81, 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]

(81−59, 81, 171)-Net over F₂₅ — Digital

Digital (22, 81, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 81, 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]

(81−59, 81, 3478)-Net in Base 25 — Upper bound on s

There is no (22, 81, 3479)-net in base 25, because

1 times m-reduction [i] would yield (22, 80, 3479)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 6865 118171 594479 581956 825444 365354 893105 739165 389590 020469 376992 136707 109241 037695 181774 303349 629202 384351 346825 > 25⁸⁰ [i]