MinT - Best Known (82, 82+30, s)-Nets in Base 9

Best Known (82, 82+30, s)-Nets in Base 9

(82, 82+30, 772)-Net over F₉ — Constructive and digital

Digital (82, 112, 772)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (5, 20, 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 (62, 92, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 46, 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]

(82, 82+30, 7084)-Net over F₉ — Digital

Digital (82, 112, 7084)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+30, large)-Net in Base 9 — Upper bound on s

There is no (82, 112, large)-net in base 9, because

28 times m-reduction [i] would yield (82, 84, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]