MinT - Best Known (99, 99+33, s)-Nets in Base 9

Best Known (99, 99+33, s)-Nets in Base 9

(99, 99+33, 940)-Net over F₉ — Constructive and digital

Digital (99, 132, 940)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (18, 34, 200)-net over F₉, using
  - trace code for nets [i] based on digital (1, 17, 100)-net over F₈₁, using
    - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
2. digital (65, 98, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 49, 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]

(99, 99+33, 13821)-Net over F₉ — Digital

Digital (99, 132, 13821)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+33, large)-Net in Base 9 — Upper bound on s

There is no (99, 132, large)-net in base 9, because

31 times m-reduction [i] would yield (99, 101, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]