MinT - Best Known (134−55, 134, s)-Nets in Base 8

Best Known (134−55, 134, s)-Nets in Base 8

(134−55, 134, 354)-Net over F₈ — Constructive and digital

Digital (79, 134, 354)-net over F₈, using

10 times m-reduction [i] based on digital (79, 144, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 72, 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]

(134−55, 134, 516)-Net over F₈ — Digital

Digital (79, 134, 516)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−55, 134, 43822)-Net in Base 8 — Upper bound on s

There is no (79, 134, 43823)-net in base 8, because

1 times m-reduction [i] would yield (79, 133, 43823)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 291606 650053 065322 362574 533544 013818 356057 167839 390598 416827 993546 726847 084173 772913 730612 529377 847584 642834 423428 709784 > 8¹³³ [i]