MinT - Best Known (58, 58+42, s)-Nets in Base 8

Best Known (58, 58+42, s)-Nets in Base 8

(58, 58+42, 354)-Net over F₈ — Constructive and digital

Digital (58, 100, 354)-net over F₈, using

2 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+42, 367)-Net over F₈ — Digital

Digital (58, 100, 367)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+42, 24751)-Net in Base 8 — Upper bound on s

There is no (58, 100, 24752)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 038539 472031 090937 836933 634678 462564 620365 320293 178651 201145 756877 083868 552734 629521 115530 > 8¹⁰⁰ [i]