MinT - Best Known (66, 66+39, s)-Nets in Base 25

Best Known (66, 66+39, s)-Nets in Base 25

(66, 66+39, 378)-Net over F₂₅ — Constructive and digital

Digital (66, 105, 378)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (22, 41, 178)-net over F₂₅, using
  - (u,Â u+v)-construction [i] based on
    1. digital (3, 12, 52)-net over F₂₅, using
      - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
        a function field by GarcÃa and Quoos [i]
    2. digital (10, 29, 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]
2. digital (25, 64, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(66, 66+39, 4583)-Net over F₂₅ — Digital

Digital (66, 105, 4583)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+39, large)-Net in Base 25 — Upper bound on s

There is no (66, 105, large)-net in base 25, because

37 times m-reduction [i] would yield (66, 68, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]