MinT - Best Known (12, 12+50, s)-Nets in Base 9

Best Known (12, 12+50, s)-Nets in Base 9

(12, 12+50, 40)-Net over F₉ — Constructive and digital

Digital (12, 62, 40)-net over F₉, using

t-expansion [i] based on digital (8, 62, 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]

(12, 12+50, 56)-Net over F₉ — Digital

Digital (12, 62, 56)-net over F₉, using

net from sequence [i] based on digital (12, 55)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 12 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(12, 12+50, 264)-Net in Base 9 — Upper bound on s

There is no (12, 62, 265)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶², 265, S₉, 50), but
- the linear programming bound shows that MÂ â‰¥ 42 606879 590678 363898 661401 259444 047906 527042 467932 899054 697298 454480 705373 840880 064434 763747 636395 549080 980461 323957 349057 616547 215625 / 287 768550 163370 509234 541407 875798 994438 779278 220097 180703 658295 559002 245659 > 9⁶² [i]