MinT - Best Known (50−39, 50, s)-Nets in Base 9

Best Known (50−39, 50, s)-Nets in Base 9

(50−39, 50, 40)-Net over F₉ — Constructive and digital

Digital (11, 50, 40)-net over F₉, using

t-expansion [i] based on digital (8, 50, 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]

(50−39, 50, 55)-Net over F₉ — Digital

Digital (11, 50, 55)-net over F₉, using

net from sequence [i] based on digital (11, 54)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 11 and N(F) ≥ 55, using
  - a curve from the manYPoints database [i]

(50−39, 50, 274)-Net in Base 9 — Upper bound on s

There is no (11, 50, 275)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁰, 275, S₉, 39), but
- the linear programming bound shows that MÂ â‰¥ 36 613743 958046 301797 391433 849834 114258 623838 123369 490870 893917 455800 906114 353872 493983 755362 519873 / 69 076050 427866 151907 405430 576191 026962 682717 471289 > 9⁵⁰ [i]