MinT - Best Known (70−25, 70, s)-Nets in Base 25

Best Known (70−25, 70, s)-Nets in Base 25

(70−25, 70, 318)-Net over F₂₅ — Constructive and digital

Digital (45, 70, 318)-net over F₂₅, using

1 times m-reduction [i] based on digital (45, 71, 318)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (4, 12, 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 (10, 23, 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, 36, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(70−25, 70, 4893)-Net over F₂₅ — Digital

Digital (45, 70, 4893)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−25, 70, large)-Net in Base 25 — Upper bound on s

There is no (45, 70, large)-net in base 25, because

23 times m-reduction [i] would yield (45, 47, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]