MinT - Best Known (77−28, 77, s)-Nets in Base 25

Best Known (77−28, 77, s)-Nets in Base 25

(77−28, 77, 326)-Net over F₂₅ — Constructive and digital

Digital (49, 77, 326)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (10, 24, 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, 53, 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]

(77−28, 77, 4428)-Net over F₂₅ — Digital

Digital (49, 77, 4428)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−28, 77, large)-Net in Base 25 — Upper bound on s

There is no (49, 77, large)-net in base 25, because

26 times m-reduction [i] would yield (49, 51, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]