MinT - Best Known (59−36, 59, s)-Nets in Base 25

Best Known (59−36, 59, s)-Nets in Base 25

(59−36, 59, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 59, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 59, 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]

(59−36, 59, 176)-Net over F₂₅ — Digital

Digital (23, 59, 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]

(59−36, 59, 12014)-Net in Base 25 — Upper bound on s

There is no (23, 59, 12015)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 30095 682329 388793 482160 577503 603161 486284 219469 111349 826923 657252 157228 523511 231825 > 25⁵⁹ [i]