MinT - Best Known (89−23, 89, s)-Nets in Base 9

Best Known (89−23, 89, s)-Nets in Base 9

(89−23, 89, 750)-Net over F₉ — Constructive and digital

Digital (66, 89, 750)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 11, 10)-net over F₉, using
  - net from sequence [i] based on digital (0, 9)-sequence over F₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 0 and N(F) ≥ 10, using
      - the rational function field F₉(x) [i]
    - Niederreiter sequence [i]
2. digital (55, 78, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 39, 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]

(89−23, 89, 8216)-Net over F₉ — Digital

Digital (66, 89, 8216)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−23, 89, large)-Net in Base 9 — Upper bound on s

There is no (66, 89, large)-net in base 9, because

21 times m-reduction [i] would yield (66, 68, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]