MinT - Best Known (57, 57+35, s)-Nets in Base 25

Best Known (57, 57+35, s)-Nets in Base 25

(57, 57+35, 356)-Net over F₂₅ — Constructive and digital

Digital (57, 92, 356)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (9, 20, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]
2. digital (10, 27, 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, 45, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(57, 57+35, 3436)-Net over F₂₅ — Digital

Digital (57, 92, 3436)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+35, large)-Net in Base 25 — Upper bound on s

There is no (57, 92, large)-net in base 25, because

33 times m-reduction [i] would yield (57, 59, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]