MinT - Best Known (13, 13+78, s)-Nets in Base 8

Best Known (13, 13+78, s)-Nets in Base 8

(13, 13+78, 48)-Net over F₈ — Constructive and digital

Digital (13, 91, 48)-net over F₈, using

t-expansion [i] based on digital (11, 91, 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, 13+78, 56)-Net over F₈ — Digital

Digital (13, 91, 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, 13+78, 119)-Net in Base 8 — Upper bound on s

There is no (13, 91, 120)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁹¹, 120, S₈, 78), but
- the linear programming bound shows that MÂ â‰¥ 48 962346 372388 992078 959777 620363 941576 318477 556578 304591 372680 016466 209851 362861 190264 714537 432419 607265 673216 / 3225 988870 909759 198984 159225 > 8⁹¹ [i]