MinT - Best Known (85−41, 85, s)-Nets in Base 8

Best Known (85−41, 85, s)-Nets in Base 8

(85−41, 85, 160)-Net over F₈ — Constructive and digital

Digital (44, 85, 160)-net over F₈, using

1 times m-reduction [i] based on digital (44, 86, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 43, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(85−41, 85, 177)-Net over F₈ — Digital

Digital (44, 85, 177)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−41, 85, 7352)-Net in Base 8 — Upper bound on s

There is no (44, 85, 7353)-net in base 8, because

1 times m-reduction [i] would yield (44, 84, 7353)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7239 436591 943889 066556 663029 577462 610878 822675 331724 799438 067389 848674 065846 > 8⁸⁴ [i]