MinT - Best Known (56−43, 56, s)-Nets in Base 8

Best Known (56−43, 56, s)-Nets in Base 8

(56−43, 56, 48)-Net over F₈ — Constructive and digital

Digital (13, 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]

(56−43, 56, 56)-Net over F₈ — Digital

Digital (13, 56, 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]

(56−43, 56, 273)-Net in Base 8 — Upper bound on s

There is no (13, 56, 274)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵⁶, 274, S₈, 43), but
- the linear programming bound shows that MÂ â‰¥ 83411 075267 075131 592230 562244 738798 269078 648256 555771 076755 360881 096242 826226 837150 007145 639846 797639 680000 / 214 644639 665348 473446 259094 394561 919952 711782 288566 402533 > 8⁵⁶ [i]