MinT - Best Known (13, 13+80, s)-Nets in Base 8

Best Known (13, 13+80, s)-Nets in Base 8

(13, 13+80, 48)-Net over F₈ — Constructive and digital

Digital (13, 93, 48)-net over F₈, using

t-expansion [i] based on digital (11, 93, 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+80, 56)-Net over F₈ — Digital

Digital (13, 93, 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+80, 112)-Net in Base 8 — Upper bound on s

There is no (13, 93, 113)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁹³, 113, S₈, 80), but
- the linear programming bound shows that MÂ â‰¥ 3516 702229 979189 814489 319589 096412 382632 708635 754519 854308 252734 396557 454730 355158 744988 541433 547614 846976 / 3131 285605 469458 705125 > 8⁹³ [i]