MinT - Best Known (167−44, 167, s)-Nets in Base 8

Best Known (167−44, 167, s)-Nets in Base 8

(167−44, 167, 1040)-Net over F₈ — Constructive and digital

Digital (123, 167, 1040)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 23, 14)-net over F₈, using
  - net from sequence [i] based on digital (1, 13)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
      - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
2. digital (100, 144, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 72, 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]

(167−44, 167, 7779)-Net over F₈ — Digital

Digital (123, 167, 7779)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−44, 167, large)-Net in Base 8 — Upper bound on s

There is no (123, 167, large)-net in base 8, because

42 times m-reduction [i] would yield (123, 125, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]