MinT - Best Known (113−30, 113, s)-Nets in Base 9

Best Known (113−30, 113, s)-Nets in Base 9

(113−30, 113, 774)-Net over F₉ — Constructive and digital

Digital (83, 113, 774)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (6, 21, 34)-net over F₉, using
  - net from sequence [i] based on digital (6, 33)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [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]

(113−30, 113, 7640)-Net over F₉ — Digital

Digital (83, 113, 7640)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−30, 113, large)-Net in Base 9 — Upper bound on s

There is no (83, 113, large)-net in base 9, because

28 times m-reduction [i] would yield (83, 85, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]