MinT - Best Known (85−73, 85, s)-Nets in Base 8

Best Known (85−73, 85, s)-Nets in Base 8

(85−73, 85, 48)-Net over F₈ — Constructive and digital

Digital (12, 85, 48)-net over F₈, using

t-expansion [i] based on digital (11, 85, 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]

(85−73, 85, 49)-Net over F₈ — Digital

Digital (12, 85, 49)-net over F₈, using

net from sequence [i] based on digital (12, 48)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 12 and N(F) ≥ 49, using
  - a curve from the manYPoints database [i]

(85−73, 85, 114)-Net in Base 8 — Upper bound on s

There is no (12, 85, 115)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁸⁵, 115, S₈, 73), but
- the linear programming bound shows that MÂ â‰¥ 181923 534783 296633 807268 342435 695639 446451 432244 559689 583645 258516 634231 769443 871143 458337 470200 578519 616802 783232 / 2 897076 268060 144144 052609 834714 395985 > 8⁸⁵ [i]