MinT - Best Known (10, 10+39, s)-Nets in Base 9

Best Known (10, 10+39, s)-Nets in Base 9

(10, 10+39, 40)-Net over F₉ — Constructive and digital

Digital (10, 49, 40)-net over F₉, using

t-expansion [i] based on digital (8, 49, 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]

(10, 10+39, 54)-Net over F₉ — Digital

Digital (10, 49, 54)-net over F₉, using

net from sequence [i] based on digital (10, 53)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
  - a curve from the manYPoints database [i]

(10, 10+39, 243)-Net in Base 9 — Upper bound on s

There is no (10, 49, 244)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁴⁹, 244, S₉, 39), but
- the linear programming bound shows that MÂ â‰¥ 34283 082352 795244 262958 614449 227548 647301 746302 468779 856618 627950 194076 013481 320016 009388 159620 561250 / 579623 210595 385894 732875 106200 962475 950760 137737 634651 > 9⁴⁹ [i]