MinT - Best Known (67, 67+47, s)-Nets in Base 8

Best Known (67, 67+47, s)-Nets in Base 8

(67, 67+47, 354)-Net over F₈ — Constructive and digital

Digital (67, 114, 354)-net over F₈, using

6 times m-reduction [i] based on digital (67, 120, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 60, 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]

(67, 67+47, 450)-Net over F₈ — Digital

Digital (67, 114, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 57, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(67, 67+47, 36822)-Net in Base 8 — Upper bound on s

There is no (67, 114, 36823)-net in base 8, because

1 times m-reduction [i] would yield (67, 113, 36823)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 120405 789479 452625 111884 247211 684728 893572 416280 401249 005430 916267 106747 614162 515809 781294 312499 447896 > 8¹¹³ [i]