MinT - Best Known (54−43, 54, s)-Nets in Base 9

Best Known (54−43, 54, s)-Nets in Base 9

(54−43, 54, 40)-Net over F₉ — Constructive and digital

Digital (11, 54, 40)-net over F₉, using

t-expansion [i] based on digital (8, 54, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(54−43, 54, 55)-Net over F₉ — Digital

Digital (11, 54, 55)-net over F₉, using

net from sequence [i] based on digital (11, 54)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 11 and N(F) ≥ 55, using
  - a curve from the manYPoints database [i]

(54−43, 54, 259)-Net in Base 9 — Upper bound on s

There is no (11, 54, 260)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁴, 260, S₉, 43), but
- the linear programming bound shows that MÂ â‰¥ 1852 629242 742438 979162 204068 234514 099886 077927 993367 356631 384826 643466 189229 880172 444972 631450 308310 630912 / 531933 426830 213143 986588 446785 089947 655782 988695 422883 > 9⁵⁴ [i]