MinT - Best Known (13, 57, s)-Nets in Base 8

Best Known (13, 57, s)-Nets in Base 8

(13, 57, 48)-Net over F₈ — Constructive and digital

Digital (13, 57, 48)-net over F₈, using

t-expansion [i] based on digital (11, 57, 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]

(13, 57, 56)-Net over F₈ — Digital

Digital (13, 57, 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]

(13, 57, 265)-Net in Base 8 — Upper bound on s

There is no (13, 57, 266)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁷, 266, S₈, 44), but
- the linear programming bound shows that MÂ â‰¥ 1 684753 441256 018563 644208 435329 831620 893657 736079 913241 531945 649699 562746 759364 660080 108939 072931 627008 000000 / 553 240987 174121 362400 387850 355619 178756 956683 316452 020781 > 8⁵⁷ [i]