MinT - Best Known (58, 58+39, s)-Nets in Base 8

Best Known (58, 58+39, s)-Nets in Base 8

(58, 58+39, 354)-Net over F₈ — Constructive and digital

Digital (58, 97, 354)-net over F₈, using

5 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+39, 442)-Net over F₈ — Digital

Digital (58, 97, 442)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+39, 41397)-Net in Base 8 — Upper bound on s

There is no (58, 97, 41398)-net in base 8, because

1 times m-reduction [i] would yield (58, 96, 41398)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 497 405266 022883 453020 255850 466021 125979 447697 466184 754341 688197 632569 172581 504371 326674 > 8⁹⁶ [i]