MinT - Best Known (92−79, 92, s)-Nets in Base 8

Best Known (92−79, 92, s)-Nets in Base 8

(92−79, 92, 48)-Net over F₈ — Constructive and digital

Digital (13, 92, 48)-net over F₈, using

t-expansion [i] based on digital (11, 92, 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]

(92−79, 92, 56)-Net over F₈ — Digital

Digital (13, 92, 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]

(92−79, 92, 118)-Net in Base 8 — Upper bound on s

There is no (13, 92, 119)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁹², 119, S₈, 79), but
- the linear programming bound shows that MÂ â‰¥ 129 999546 883962 058358 004388 065873 679449 694206 901508 052609 978819 742873 650279 964528 450482 827779 786342 569147 891712 / 926 694950 219999 545905 681075 > 8⁹² [i]