MinT - Best Known (12, 54, s)-Nets in Base 8

Best Known (12, 54, s)-Nets in Base 8

(12, 54, 48)-Net over F₈ — Constructive and digital

Digital (12, 54, 48)-net over F₈, using

t-expansion [i] based on digital (11, 54, 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]

(12, 54, 49)-Net over F₈ — Digital

Digital (12, 54, 49)-net over F₈, using

net from sequence [i] based on digital (12, 48)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 12 and N(F) ≥ 49, using
  - a curve from the manYPoints database [i]

(12, 54, 244)-Net in Base 8 — Upper bound on s

There is no (12, 54, 245)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁴, 245, S₈, 42), but
- the linear programming bound shows that MÂ â‰¥ 1 057368 982503 016130 475324 671746 524898 024594 217471 847562 230647 826292 591859 696769 971793 300385 589822 887034 880000 / 172899 556177 026823 444056 708013 798026 259629 956649 908682 937547 > 8⁵⁴ [i]