MinT - Best Known (12, 59, s)-Nets in Base 9

Best Known (12, 59, s)-Nets in Base 9

(12, 59, 40)-Net over F₉ — Constructive and digital

Digital (12, 59, 40)-net over F₉, using

t-expansion [i] based on digital (8, 59, 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, 59, 56)-Net over F₉ — Digital

Digital (12, 59, 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, 59, 277)-Net in Base 9 — Upper bound on s

There is no (12, 59, 278)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁹, 278, S₉, 47), but
- the linear programming bound shows that MÂ â‰¥ 1302 616387 238764 395312 729107 927351 605765 145077 730221 219327 182185 121455 202811 846670 035371 561530 032248 278114 838828 712125 / 6 128712 372776 642304 790423 792968 038861 205631 944824 101549 760438 > 9⁵⁹ [i]