MinT - Best Known (110−26, 110, s)-Nets in Base 7

Best Known (110−26, 110, s)-Nets in Base 7

(110−26, 110, 699)-Net over F₇ — Constructive and digital

Digital (84, 110, 699)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (3, 16, 11)-net over F₇, using
  - net from sequence [i] based on digital (3, 10)-sequence over F₇, using
    - Niederreiter sequence [i]
  - Niederreiter sequence (Bratleyâ€“Foxâ€“Niederreiter implementation) with equidistant coordinate [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]

(110−26, 110, 8882)-Net over F₇ — Digital

Digital (84, 110, 8882)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−26, 110, large)-Net in Base 7 — Upper bound on s

There is no (84, 110, large)-net in base 7, because

24 times m-reduction [i] would yield (84, 86, large)-net in base 7, but
- mutually orthogonal hypercube bound [i]