MinT - Best Known (138−131, 138, s)-Nets in Base 9

Best Known (138−131, 138, s)-Nets in Base 9

(138−131, 138, 36)-Net over F₉ — Constructive and digital

Digital (7, 138, 36)-net over F₉, using

net from sequence [i] based on digital (7, 35)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
  - a function field by SÃ©mirat [i]

(138−131, 138, 40)-Net over F₉ — Digital

Digital (7, 138, 40)-net over F₉, using

net from sequence [i] based on digital (7, 39)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 40, using
  - a curve from the manYPoints database [i]

(138−131, 138, 73)-Net in Base 9 — Upper bound on s

There is no (7, 138, 74)-net in base 9, because

71 times m-reduction [i] would yield (7, 67, 74)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9⁶⁷, 74, S₉, 60), but
  - the linear programming bound shows that MÂ â‰¥ 985656 408650 624771 763245 030155 475596 055326 621140 743196 169188 696976 053441 / 111 718145 > 9⁶⁷ [i]