MinT - Best Known (12, 12+52, s)-Nets in Base 9

Best Known (12, 12+52, s)-Nets in Base 9

(12, 12+52, 40)-Net over F₉ — Constructive and digital

Digital (12, 64, 40)-net over F₉, using

t-expansion [i] based on digital (8, 64, 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+52, 56)-Net over F₉ — Digital

Digital (12, 64, 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+52, 261)-Net in Base 9 — Upper bound on s

There is no (12, 64, 262)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶⁴, 262, S₉, 52), but
- the linear programming bound shows that MÂ â‰¥ 12 990621 612543 326804 332013 445708 471100 068512 952374 505418 911059 331520 489865 692987 938290 140227 569967 698126 987656 304599 774733 400889 221359 064375 / 1 088138 426450 258559 313329 440594 525137 110484 835902 878835 611206 211192 732979 888039 > 9⁶⁴ [i]