MinT - Best Known (10, 10+41, s)-Nets in Base 9

Best Known (10, 10+41, s)-Nets in Base 9

(10, 10+41, 40)-Net over F₉ — Constructive and digital

Digital (10, 51, 40)-net over F₉, using

t-expansion [i] based on digital (8, 51, 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+41, 54)-Net over F₉ — Digital

Digital (10, 51, 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+41, 234)-Net in Base 9 — Upper bound on s

There is no (10, 51, 235)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵¹, 235, S₉, 41), but
- the linear programming bound shows that MÂ â‰¥ 2 848880 717187 902127 983030 032262 388466 820408 074764 158910 574332 029568 594494 136301 038752 852370 981154 251600 / 595894 630941 027491 427276 782542 936823 246172 808085 753773 > 9⁵¹ [i]