MinT - Best Known (12, 12+85, s)-Nets in Base 9

Best Known (12, 12+85, s)-Nets in Base 9

(12, 12+85, 40)-Net over F₉ — Constructive and digital

Digital (12, 97, 40)-net over F₉, using

t-expansion [i] based on digital (8, 97, 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+85, 56)-Net over F₉ — Digital

Digital (12, 97, 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+85, 118)-Net in Base 9 — Upper bound on s

There is no (12, 97, 119)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁹⁷, 119, S₉, 85), but
- the linear programming bound shows that MÂ â‰¥ 1 356113 119788 100555 369499 438225 755368 152523 523169 385919 223112 809697 856332 976595 175567 178893 462566 370924 138268 930311 / 2702 353938 094627 396255 > 9⁹⁷ [i]