MinT - Best Known (126, 169, s)-Nets in Base 8

Best Known (126, 169, s)-Nets in Base 8

(126, 169, 1054)-Net over F₈ — Constructive and digital

Digital (126, 169, 1054)-net over F₈, using

8¹ times duplication [i] based on digital (125, 168, 1054)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 26, 28)-net over F₈, using
    - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
        a function field by SÃ©mirat [i]
  2. digital (99, 142, 1026)-net over F₈, using
    - trace code for nets [i] based on digital (28, 71, 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]

(126, 169, 10173)-Net over F₈ — Digital

Digital (126, 169, 10173)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 169, large)-Net in Base 8 — Upper bound on s

There is no (126, 169, large)-net in base 8, because

41 times m-reduction [i] would yield (126, 128, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]