MinT - Best Known (87−33, 87, s)-Nets in Base 25

Best Known (87−33, 87, s)-Nets in Base 25

(87−33, 87, 326)-Net over F₂₅ — Constructive and digital

Digital (54, 87, 326)-net over F₂₅, using

5 times m-reduction [i] based on digital (54, 92, 326)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. 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, 63, 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]

(87−33, 87, 3384)-Net over F₂₅ — Digital

Digital (54, 87, 3384)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−33, 87, large)-Net in Base 25 — Upper bound on s

There is no (54, 87, large)-net in base 25, because

31 times m-reduction [i] would yield (54, 56, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]