MinT - Best Known (13, 13+77, s)-Nets in Base 8

Best Known (13, 13+77, s)-Nets in Base 8

(13, 13+77, 48)-Net over F₈ — Constructive and digital

Digital (13, 90, 48)-net over F₈, using

t-expansion [i] based on digital (11, 90, 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+77, 56)-Net over F₈ — Digital

Digital (13, 90, 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+77, 129)-Net in Base 8 — Upper bound on s

There is no (13, 90, 130)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁹⁰, 130, S₈, 77), but
- the linear programming bound shows that MÂ â‰¥ 722 192362 919325 363496 696570 081377 868415 015325 877966 815393 186903 190147 686497 377809 559177 986850 477135 627050 280096 877894 434816 / 371866 070353 772264 120281 941722 778381 000075 > 8⁹⁰ [i]