MinT - Best Known (158−64, 158, s)-Nets in Base 8

Best Known (158−64, 158, s)-Nets in Base 8

(158−64, 158, 354)-Net over F₈ — Constructive and digital

Digital (94, 158, 354)-net over F₈, using

t-expansion [i] based on digital (93, 158, 354)-net over F₈, using
- 14 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(158−64, 158, 384)-Net in Base 8 — Constructive

(94, 158, 384)-net in base 8, using

trace code for nets [i] based on (15, 79, 192)-net in base 64, using
- 5 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
  - base change [i] based on digital (3, 72, 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]

(158−64, 158, 630)-Net over F₈ — Digital

Digital (94, 158, 630)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−64, 158, 52556)-Net in Base 8 — Upper bound on s

There is no (94, 158, 52557)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48803 329999 597929 289349 772502 650708 112952 592280 151503 588415 990638 738879 461220 438615 402759 661783 890747 739629 418596 602652 783920 939156 784637 133270 > 8¹⁵⁸ [i]