MinT - Best Known (58, 58+37, s)-Nets in Base 8

Best Known (58, 58+37, s)-Nets in Base 8

(58, 58+37, 354)-Net over F₈ — Constructive and digital

Digital (58, 95, 354)-net over F₈, using

7 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+37, 384)-Net in Base 8 — Constructive

(58, 95, 384)-net in base 8, using

1 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+37, 510)-Net over F₈ — Digital

Digital (58, 95, 510)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+37, 56115)-Net in Base 8 — Upper bound on s

There is no (58, 95, 56116)-net in base 8, because

1 times m-reduction [i] would yield (58, 94, 56116)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7 771887 184948 194053 948246 767921 900263 066264 593106 911447 511778 951380 948667 890045 415805 > 8⁹⁴ [i]