MinT - Best Known (138−122, 138, s)-Nets in Base 9

Best Known (138−122, 138, s)-Nets in Base 9

(138−122, 138, 64)-Net over F₉ — Constructive and digital

Digital (16, 138, 64)-net over F₉, using

t-expansion [i] based on digital (13, 138, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(138−122, 138, 74)-Net over F₉ — Digital

Digital (16, 138, 74)-net over F₉, using

net from sequence [i] based on digital (16, 73)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 16 and N(F) ≥ 74, using
  - a curve from the manYPoints database [i]

(138−122, 138, 143)-Net in Base 9 — Upper bound on s

There is no (16, 138, 144)-net in base 9, because

12 times m-reduction [i] would yield (16, 126, 144)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9¹²⁶, 144, S₉, 110), but
  - the linear programming bound shows that MÂ â‰¥ 13985 352127 709815 135823 207322 213660 655679 036196 057151 464807 486617 148753 068973 647813 060841 422573 871412 475846 092090 726797 721652 094761 117031 / 7512 322263 802055 > 9¹²⁶ [i]