MinT - Best Known (67−24, 67, s)-Nets in Base 25

Best Known (67−24, 67, s)-Nets in Base 25

(67−24, 67, 304)-Net over F₂₅ — Constructive and digital

Digital (43, 67, 304)-net over F₂₅, using

1 times m-reduction [i] based on digital (43, 68, 304)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (3, 11, 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, 22, 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]
  3. digital (10, 35, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(67−24, 67, 4651)-Net over F₂₅ — Digital

Digital (43, 67, 4651)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67−24, 67, large)-Net in Base 25 — Upper bound on s

There is no (43, 67, large)-net in base 25, because

22 times m-reduction [i] would yield (43, 45, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]