MinT - Best Known (56−44, 56, s)-Nets in Base 8

Best Known (56−44, 56, s)-Nets in Base 8

(56−44, 56, 48)-Net over F₈ — Constructive and digital

Digital (12, 56, 48)-net over F₈, using

t-expansion [i] based on digital (11, 56, 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]

(56−44, 56, 49)-Net over F₈ — Digital

Digital (12, 56, 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]

(56−44, 56, 237)-Net in Base 8 — Upper bound on s

There is no (12, 56, 238)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁶, 238, S₈, 44), but
- the linear programming bound shows that MÂ â‰¥ 25 573244 863544 060785 975297 974438 122076 282672 176639 270811 421164 691283 984882 478389 816308 618568 369544 692949 319680 / 65914 286156 042213 250920 496026 141953 275284 052389 004987 749473 > 8⁵⁶ [i]