MinT - Best Known (11, 11+74, s)-Nets in Base 9

Best Known (11, 11+74, s)-Nets in Base 9

(11, 11+74, 40)-Net over F₉ — Constructive and digital

Digital (11, 85, 40)-net over F₉, using

t-expansion [i] based on digital (8, 85, 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]

(11, 11+74, 55)-Net over F₉ — Digital

Digital (11, 85, 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]

(11, 11+74, 140)-Net in Base 9 — Upper bound on s

There is no (11, 85, 141)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁸⁵, 141, S₉, 74), but
- the linear programming bound shows that MÂ â‰¥ 1 640244 463417 620391 007151 187213 824098 229143 473573 991804 963173 464102 127207 331504 792830 833762 125892 050177 377493 943253 263381 003792 915144 724341 567712 001028 722744 316969 / 1257 911773 577742 532965 268980 379475 651128 476937 663631 978621 348153 294330 609637 859225 > 9⁸⁵ [i]