MinT - Best Known (54, 54+37, s)-Nets in Base 8

Best Known (54, 54+37, s)-Nets in Base 8

(54, 54+37, 354)-Net over F₈ — Constructive and digital

Digital (54, 91, 354)-net over F₈, using

3 times m-reduction [i] based on digital (54, 94, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 47, 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]

(54, 54+37, 399)-Net over F₈ — Digital

Digital (54, 91, 399)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+37, 35346)-Net in Base 8 — Upper bound on s

There is no (54, 91, 35347)-net in base 8, because

1 times m-reduction [i] would yield (54, 90, 35347)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1897 656919 703967 834667 394604 197189 364607 453322 321905 607888 533542 165605 796761 392561 > 8⁹⁰ [i]