MinT - Best Known (166−69, 166, s)-Nets in Base 8

Best Known (166−69, 166, s)-Nets in Base 8

(166−69, 166, 354)-Net over F₈ — Constructive and digital

Digital (97, 166, 354)-net over F₈, using

t-expansion [i] based on digital (93, 166, 354)-net over F₈, using
- 6 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]

(166−69, 166, 583)-Net over F₈ — Digital

Digital (97, 166, 583)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−69, 166, 46646)-Net in Base 8 — Upper bound on s

There is no (97, 166, 46647)-net in base 8, because

1 times m-reduction [i] would yield (97, 165, 46647)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 102313 571161 262187 224202 689299 410855 196125 843766 171503 450879 968467 883260 741501 254562 186128 206203 079243 493866 066559 434755 220661 122864 531475 031021 105441 > 8¹⁶⁵ [i]