MinT - Best Known (160−61, 160, s)-Nets in Base 8

Best Known (160−61, 160, s)-Nets in Base 8

(160−61, 160, 354)-Net over F₈ — Constructive and digital

Digital (99, 160, 354)-net over F₈, using

t-expansion [i] based on digital (93, 160, 354)-net over F₈, using
- 12 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]

(160−61, 160, 432)-Net in Base 8 — Constructive

(99, 160, 432)-net in base 8, using

4 times m-reduction [i] based on (99, 164, 432)-net in base 8, using
- trace code for nets [i] based on (17, 82, 216)-net in base 64, using
  - 2 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
    - base change [i] based on digital (5, 72, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(160−61, 160, 853)-Net over F₈ — Digital

Digital (99, 160, 853)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−61, 160, 105193)-Net in Base 8 — Upper bound on s

There is no (99, 160, 105194)-net in base 8, because

1 times m-reduction [i] would yield (99, 159, 105194)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 390244 314321 294973 302692 561841 869443 949153 690132 842439 400080 524821 505942 425462 704809 621312 163737 739838 595232 825707 506427 300203 062409 097321 442288 > 8¹⁵⁹ [i]