MinT - Best Known (140−35, 140, s)-Nets in Base 9

Best Known (140−35, 140, s)-Nets in Base 9

(140−35, 140, 972)-Net over F₉ — Constructive and digital

Digital (105, 140, 972)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (21, 38, 232)-net over F₉, using
  - trace code for nets [i] based on digital (2, 19, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]
2. digital (67, 102, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 51, 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]

(140−35, 140, 14392)-Net over F₉ — Digital

Digital (105, 140, 14392)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−35, 140, large)-Net in Base 9 — Upper bound on s

There is no (105, 140, large)-net in base 9, because

33 times m-reduction [i] would yield (105, 107, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]