MinT - Best Known (171−40, 171, s)-Nets in Base 8

Best Known (171−40, 171, s)-Nets in Base 8

(171−40, 171, 1091)-Net over F₈ — Constructive and digital

Digital (131, 171, 1091)-net over F₈, using

1 times m-reduction [i] based on digital (131, 172, 1091)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 34, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]
  2. digital (97, 138, 1026)-net over F₈, using
    - trace code for nets [i] based on digital (28, 69, 513)-net over F₆₄, using
      - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(171−40, 171, 20065)-Net over F₈ — Digital

Digital (131, 171, 20065)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−40, 171, large)-Net in Base 8 — Upper bound on s

There is no (131, 171, large)-net in base 8, because

38 times m-reduction [i] would yield (131, 133, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]