MinT - Best Known (51−40, 51, s)-Nets in Base 9

Best Known (51−40, 51, s)-Nets in Base 9

(51−40, 51, 40)-Net over F₉ — Constructive and digital

Digital (11, 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]

(51−40, 51, 55)-Net over F₉ — Digital

Digital (11, 51, 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]

(51−40, 51, 269)-Net in Base 9 — Upper bound on s

There is no (11, 51, 270)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 742357 766500 882227 849203 235234 506817 391043 421249 > 9⁵¹ [i]