MinT - Best Known (81, 81+26, s)-Nets in Base 7

Best Known (81, 81+26, s)-Nets in Base 7

(81, 81+26, 696)-Net over F₇ — Constructive and digital

Digital (81, 107, 696)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (0, 13, 8)-net over F₇, using
  - net from sequence [i] based on digital (0, 7)-sequence over F₇, using
    - Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using
      - the rational function field F₇(x) [i]
    - Niederreiter sequence [i]
2. digital (68, 94, 688)-net over F₇, using
  - trace code for nets [i] based on digital (21, 47, 344)-net over F₄₉, using
    - net from sequence [i] based on digital (21, 343)-sequence over F₄₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 21 and N(F) ≥ 344, using
        the Hermitian function field over F₄₉ [i]

(81, 81+26, 7035)-Net over F₇ — Digital

Digital (81, 107, 7035)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+26, large)-Net in Base 7 — Upper bound on s

There is no (81, 107, large)-net in base 7, because

24 times m-reduction [i] would yield (81, 83, large)-net in base 7, but
- mutually orthogonal hypercube bound [i]