MinT - Best Known (58, 58+40, s)-Nets in Base 8

Best Known (58, 58+40, s)-Nets in Base 8

(58, 58+40, 354)-Net over F₈ — Constructive and digital

Digital (58, 98, 354)-net over F₈, using

4 times m-reduction [i] based on digital (58, 102, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 51, 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]

(58, 58+40, 418)-Net over F₈ — Digital

Digital (58, 98, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 49, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(58, 58+40, 31563)-Net in Base 8 — Upper bound on s

There is no (58, 98, 31564)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 31847 568328 013254 487581 263881 442704 654641 611979 820987 338456 971415 088681 035894 394309 439544 > 8⁹⁸ [i]