MinT - Best Known (96−83, 96, s)-Nets in Base 8

Best Known (96−83, 96, s)-Nets in Base 8

(96−83, 96, 48)-Net over F₈ — Constructive and digital

Digital (13, 96, 48)-net over F₈, using

t-expansion [i] based on digital (11, 96, 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]

(96−83, 96, 56)-Net over F₈ — Digital

Digital (13, 96, 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]

(96−83, 96, 110)-Net in Base 8 — Upper bound on s

There is no (13, 96, 111)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁹⁶, 111, S₈, 83), but
- the linear programming bound shows that MÂ â‰¥ 104768 796124 878332 797794 124705 117581 529237 094229 976605 504710 512252 460542 688451 405499 165810 519082 795008 / 192 154076 229375 > 8⁹⁶ [i]