MinT - Best Known (107−28, 107, s)-Nets in Base 9

Best Known (107−28, 107, s)-Nets in Base 9

(107−28, 107, 772)-Net over F₉ — Constructive and digital

Digital (79, 107, 772)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 19, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. digital (60, 88, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 44, 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]

(107−28, 107, 8273)-Net over F₉ — Digital

Digital (79, 107, 8273)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−28, 107, large)-Net in Base 9 — Upper bound on s

There is no (79, 107, large)-net in base 9, because

26 times m-reduction [i] would yield (79, 81, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]