MinT - Best Known (10, 10+74, s)-Nets in Base 9

Best Known (10, 10+74, s)-Nets in Base 9

(10, 10+74, 40)-Net over F₉ — Constructive and digital

Digital (10, 84, 40)-net over F₉, using

t-expansion [i] based on digital (8, 84, 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+74, 54)-Net over F₉ — Digital

Digital (10, 84, 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+74, 100)-Net in Base 9 — Upper bound on s

There is no (10, 84, 101)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁸⁴, 101, S₉, 74), but
- the linear programming bound shows that MÂ â‰¥ 2834 164718 308637 868594 676012 056428 023190 829828 425146 840160 101471 661133 787159 796932 159401 985797 / 15 190550 827375 > 9⁸⁴ [i]