MinT - Best Known (58, 58+35, s)-Nets in Base 8

Best Known (58, 58+35, s)-Nets in Base 8

(58, 58+35, 354)-Net over F₈ — Constructive and digital

Digital (58, 93, 354)-net over F₈, using

9 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+35, 384)-Net in Base 8 — Constructive

(58, 93, 384)-net in base 8, using

3 times m-reduction [i] based on (58, 96, 384)-net in base 8, using
- trace code for nets [i] based on (10, 48, 192)-net in base 64, using
  - 1 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
    - base change [i] based on digital (3, 42, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(58, 58+35, 588)-Net over F₈ — Digital

Digital (58, 93, 588)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+35, 79086)-Net in Base 8 — Upper bound on s

There is no (58, 93, 79087)-net in base 8, because

1 times m-reduction [i] would yield (58, 92, 79087)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 121439 041080 872344 943981 607682 517624 256004 672533 190449 189530 194327 041502 562258 338876 > 8⁹² [i]