MinT - Best Known (11, 11+81, s)-Nets in Base 9

Best Known (11, 11+81, s)-Nets in Base 9

(11, 11+81, 40)-Net over F₉ — Constructive and digital

Digital (11, 92, 40)-net over F₉, using

t-expansion [i] based on digital (8, 92, 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+81, 55)-Net over F₉ — Digital

Digital (11, 92, 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+81, 106)-Net in Base 9 — Upper bound on s

There is no (11, 92, 107)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁹², 107, S₉, 81), but
- the linear programming bound shows that MÂ â‰¥ 188546 507701 542940 037830 428244 754062 708541 214725 665590 081296 582697 226030 095841 296274 450287 877654 724541 / 23 170810 285480 > 9⁹² [i]