MinT - Best Known (57−36, 57, s)-Nets in Base 25

Best Known (57−36, 57, s)-Nets in Base 25

(57−36, 57, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 57, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 57, 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]

(57−36, 57, 171)-Net over F₂₅ — Digital

Digital (21, 57, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 57, 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]

(57−36, 57, 8399)-Net in Base 25 — Upper bound on s

There is no (21, 57, 8400)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 48 204752 693669 914993 347656 455505 382829 579859 324426 295523 140052 868341 481953 777921 > 25⁵⁷ [i]