MinT - Best Known (93, 93+75, s)-Nets in Base 8

Best Known (93, 93+75, s)-Nets in Base 8

(93, 93+75, 354)-Net over F₈ — Constructive and digital

Digital (93, 168, 354)-net over F₈, using

4 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]

(93, 93+75, 432)-Net over F₈ — Digital

Digital (93, 168, 432)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+75, 24918)-Net in Base 8 — Upper bound on s

There is no (93, 168, 24919)-net in base 8, because

1 times m-reduction [i] would yield (93, 167, 24919)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 554318 922883 370730 269582 550455 546088 220155 165422 209858 384000 299631 554918 037119 229311 861941 445489 478720 826714 452196 553702 013423 020471 233306 951231 614500 > 8¹⁶⁷ [i]