MinT - Best Known (73−27, 73, s)-Nets in Base 25

Best Known (73−27, 73, s)-Nets in Base 25

(73−27, 73, 318)-Net over F₂₅ — Constructive and digital

Digital (46, 73, 318)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (4, 13, 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, 37, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(73−27, 73, 3712)-Net over F₂₅ — Digital

Digital (46, 73, 3712)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−27, 73, large)-Net in Base 25 — Upper bound on s

There is no (46, 73, large)-net in base 25, because

25 times m-reduction [i] would yield (46, 48, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]