MinT - Best Known (77−29, 77, s)-Nets in Base 25

Best Known (77−29, 77, s)-Nets in Base 25

(77−29, 77, 318)-Net over F₂₅ — Constructive and digital

Digital (48, 77, 318)-net over F₂₅, using

25¹ times duplication [i] based on digital (47, 76, 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, 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]
  3. digital (10, 39, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(77−29, 77, 3303)-Net over F₂₅ — Digital

Digital (48, 77, 3303)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−29, 77, large)-Net in Base 25 — Upper bound on s

There is no (48, 77, large)-net in base 25, because

27 times m-reduction [i] would yield (48, 50, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]