MinT - Best Known (101−27, 101, s)-Nets in Base 9

Best Known (101−27, 101, s)-Nets in Base 9

(101−27, 101, 760)-Net over F₉ — Constructive and digital

Digital (74, 101, 760)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (2, 15, 20)-net over F₉, using
  - net from sequence [i] based on digital (2, 19)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]
2. digital (59, 86, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 43, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(101−27, 101, 6728)-Net over F₉ — Digital

Digital (74, 101, 6728)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−27, 101, large)-Net in Base 9 — Upper bound on s

There is no (74, 101, large)-net in base 9, because

25 times m-reduction [i] would yield (74, 76, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]