MinT - Best Known (58−45, 58, s)-Nets in Base 8

Best Known (58−45, 58, s)-Nets in Base 8

(58−45, 58, 48)-Net over F₈ — Constructive and digital

Digital (13, 58, 48)-net over F₈, using

t-expansion [i] based on digital (11, 58, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(58−45, 58, 56)-Net over F₈ — Digital

Digital (13, 58, 56)-net over F₈, using

net from sequence [i] based on digital (13, 55)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 13 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(58−45, 58, 262)-Net in Base 8 — Upper bound on s

There is no (13, 58, 263)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁸, 263, S₈, 45), but
- the linear programming bound shows that MÂ â‰¥ 217902 256011 434052 266543 822862 202906 517259 848891 912853 344002 415033 548978 571281 068650 640851 300624 102703 759360 000000 / 8 968414 884886 931244 580807 274592 807979 029293 166233 756794 516421 > 8⁵⁸ [i]