MinT - Best Known (58, 91, s)-Nets in Base 8

Best Known (58, 91, s)-Nets in Base 8

(58, 91, 354)-Net over F₈ — Constructive and digital

Digital (58, 91, 354)-net over F₈, using

11 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, 91, 514)-Net in Base 8 — Constructive

(58, 91, 514)-net in base 8, using

1 times m-reduction [i] based on (58, 92, 514)-net in base 8, using
- base change [i] based on digital (35, 69, 514)-net over F₁₆, using
  - 1 times m-reduction [i] based on digital (35, 70, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 35, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]

(58, 91, 692)-Net over F₈ — Digital

Digital (58, 91, 692)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 91, 116757)-Net in Base 8 — Upper bound on s

There is no (58, 91, 116758)-net in base 8, because

1 times m-reduction [i] would yield (58, 90, 116758)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1897 220226 740942 957711 083304 313612 202217 994291 178353 057114 882546 824900 900753 562237 > 8⁹⁰ [i]