MinT - Best Known (90−40, 90, s)-Nets in Base 9

Best Known (90−40, 90, s)-Nets in Base 9

(90−40, 90, 320)-Net over F₉ — Constructive and digital

Digital (50, 90, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 45, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(90−40, 90, 334)-Net over F₉ — Digital

Digital (50, 90, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 45, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(90−40, 90, 20419)-Net in Base 9 — Upper bound on s

There is no (50, 90, 20420)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76 188920 415225 888513 592107 973622 001200 874034 984798 113643 332309 491524 902905 602098 320769 > 9⁹⁰ [i]