MinT - Best Known (152−59, 152, s)-Nets in Base 8

Best Known (152−59, 152, s)-Nets in Base 8

(152−59, 152, 354)-Net over F₈ — Constructive and digital

Digital (93, 152, 354)-net over F₈, using

20 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]

(152−59, 152, 432)-Net in Base 8 — Constructive

(93, 152, 432)-net in base 8, using

2 times m-reduction [i] based on (93, 154, 432)-net in base 8, using
- trace code for nets [i] based on (16, 77, 216)-net in base 64, using
  - base change [i] based on digital (5, 66, 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]

(152−59, 152, 748)-Net over F₈ — Digital

Digital (93, 152, 748)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−59, 152, 83989)-Net in Base 8 — Upper bound on s

There is no (93, 152, 83990)-net in base 8, because

1 times m-reduction [i] would yield (93, 151, 83990)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23260 781157 510058 467823 458686 346602 272195 483791 018489 180393 822733 412352 473879 063948 942592 562255 823706 451363 664812 790044 463737 622447 687936 > 8¹⁵¹ [i]