MinT - Best Known (69, 69+47, s)-Nets in Base 8

Best Known (69, 69+47, s)-Nets in Base 8

(69, 69+47, 354)-Net over F₈ — Constructive and digital

Digital (69, 116, 354)-net over F₈, using

8 times m-reduction [i] based on digital (69, 124, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 62, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(69, 69+47, 488)-Net over F₈ — Digital

Digital (69, 116, 488)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+47, 44123)-Net in Base 8 — Upper bound on s

There is no (69, 116, 44124)-net in base 8, because

1 times m-reduction [i] would yield (69, 115, 44124)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 71 699443 382689 896345 236134 234909 618800 290373 311384 545097 049912 538714 732020 213701 662200 226615 264004 892090 > 8¹¹⁵ [i]