MinT - Best Known (93, 93+32, s)-Nets in Base 9

Best Known (93, 93+32, s)-Nets in Base 9

(93, 93+32, 804)-Net over F₉ — Constructive and digital

Digital (93, 125, 804)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (13, 29, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]
2. digital (64, 96, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 48, 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]

(93, 93+32, 10947)-Net over F₉ — Digital

Digital (93, 125, 10947)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+32, large)-Net in Base 9 — Upper bound on s

There is no (93, 125, large)-net in base 9, because

30 times m-reduction [i] would yield (93, 95, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]