MinT - Best Known (13, 13+46, s)-Nets in Base 8

Best Known (13, 13+46, s)-Nets in Base 8

(13, 13+46, 48)-Net over F₈ — Constructive and digital

Digital (13, 59, 48)-net over F₈, using

t-expansion [i] based on digital (11, 59, 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+46, 56)-Net over F₈ — Digital

Digital (13, 59, 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+46, 258)-Net in Base 8 — Upper bound on s

There is no (13, 59, 259)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁹, 259, S₈, 46), but
- the linear programming bound shows that MÂ â‰¥ 826 543620 682016 769234 199554 926431 731791 288385 851428 613560 969736 411732 071209 023402 929725 177306 272157 436984 531353 600000 / 4118 263515 435640 805863 398672 551556 162028 670987 766357 108585 690079 > 8⁵⁹ [i]