MinT - Best Known (55−43, 55, s)-Nets in Base 8

Best Known (55−43, 55, s)-Nets in Base 8

(55−43, 55, 48)-Net over F₈ — Constructive and digital

Digital (12, 55, 48)-net over F₈, using

t-expansion [i] based on digital (11, 55, 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]

(55−43, 55, 49)-Net over F₈ — Digital

Digital (12, 55, 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]

(55−43, 55, 241)-Net in Base 8 — Upper bound on s

There is no (12, 55, 242)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁵, 242, S₈, 43), but
- the linear programming bound shows that MÂ â‰¥ 14464 840226 332542 547389 909871 027522 264033 663304 553572 326161 857345 472509 969848 313022 591558 909689 856000 000000 / 293 447744 665026 108389 436723 810773 649370 531261 998399 394597 > 8⁵⁵ [i]