MinT - Best Known (90−19, 90, s)-Nets in Base 5

Best Known (90−19, 90, s)-Nets in Base 5

(90−19, 90, 434)-Net over F₅ — Constructive and digital

Digital (71, 90, 434)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (23, 32, 182)-net over F₅, using
  - (u,Â u+v)-construction [i] based on
    1. digital (4, 8, 78)-net over F₅, using
      - linear code embedding found in a computer search [i]
    2. digital (15, 24, 104)-net over F₅, using
      - trace code for nets [i] based on 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 (39, 58, 252)-net over F₅, using
  - trace code for nets [i] based on 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]

(90−19, 90, 5910)-Net over F₅ — Digital

Digital (71, 90, 5910)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−19, 90, large)-Net in Base 5 — Upper bound on s

There is no (71, 90, large)-net in base 5, because

17 times m-reduction [i] would yield (71, 73, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]