MinT - Best Known (11, 11+49, s)-Nets in Base 9

Best Known (11, 11+49, s)-Nets in Base 9

(11, 11+49, 40)-Net over F₉ — Constructive and digital

Digital (11, 60, 40)-net over F₉, using

t-expansion [i] based on digital (8, 60, 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+49, 55)-Net over F₉ — Digital

Digital (11, 60, 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+49, 240)-Net in Base 9 — Upper bound on s

There is no (11, 60, 241)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶⁰, 241, S₉, 49), but
- the linear programming bound shows that MÂ â‰¥ 1 159726 669887 275891 066272 477409 986739 275111 621115 874116 023188 826964 473224 055661 727724 805201 248357 199289 636850 465259 167174 692105 / 625 133175 721058 278106 098289 002426 214731 823978 061411 259797 268255 516961 > 9⁶⁰ [i]