MinT - Best Known (110−46, 110, s)-Nets in Base 8

Best Known (110−46, 110, s)-Nets in Base 8

(110−46, 110, 354)-Net over F₈ — Constructive and digital

Digital (64, 110, 354)-net over F₈, using

4 times m-reduction [i] based on digital (64, 114, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 57, 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]

(110−46, 110, 418)-Net over F₈ — Digital

Digital (64, 110, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 55, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(110−46, 110, 28071)-Net in Base 8 — Upper bound on s

There is no (64, 110, 28072)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2188 410595 536708 133452 532421 132535 803012 033060 442585 671089 520319 179597 336091 616789 546720 942167 074426 > 8¹¹⁰ [i]