MinT - Best Known (75−54, 75, s)-Nets in Base 25

Best Known (75−54, 75, s)-Nets in Base 25

(75−54, 75, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 75, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 75, 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]

(75−54, 75, 171)-Net over F₂₅ — Digital

Digital (21, 75, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 75, 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]

(75−54, 75, 3464)-Net in Base 25 — Upper bound on s

There is no (21, 75, 3465)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 705 289649 298149 693214 788036 776719 011091 922867 805095 758789 390428 015781 249759 752565 017647 614045 378969 394057 > 25⁷⁵ [i]