MinT - Best Known (54−20, 54, s)-Nets in Base 25

Best Known (54−20, 54, s)-Nets in Base 25

(54−20, 54, 258)-Net over F₂₅ — Constructive and digital

Digital (34, 54, 258)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (4, 10, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]
2. digital (4, 14, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅ (see above)
3. digital (10, 30, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(54−20, 54, 3115)-Net over F₂₅ — Digital

Digital (34, 54, 3115)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−20, 54, 6677913)-Net in Base 25 — Upper bound on s

There is no (34, 54, 6677914)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 3081 490262 354684 280783 095357 230037 450016 989440 666278 746259 050252 100198 523681 > 25⁵⁴ [i]