MinT - Best Known (12, 86, s)-Nets in Base 8

Best Known (12, 86, s)-Nets in Base 8

(12, 86, 48)-Net over F₈ — Constructive and digital

Digital (12, 86, 48)-net over F₈, using

t-expansion [i] based on digital (11, 86, 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, 86, 49)-Net over F₈ — Digital

Digital (12, 86, 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, 86, 109)-Net in Base 8 — Upper bound on s

There is no (12, 86, 110)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁸⁶, 110, S₈, 74), but
- the linear programming bound shows that MÂ â‰¥ 24837 277551 195515 418416 760254 609340 122637 003998 201349 467100 276783 591858 755747 571411 840665 790885 920768 / 51565 021303 874708 057175 > 8⁸⁶ [i]