MinT - Best Known (54−22, 54, s)-Nets in Base 9

Best Known (54−22, 54, s)-Nets in Base 9

(54−22, 54, 320)-Net over F₉ — Constructive and digital

Digital (32, 54, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 27, 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]

(54−22, 54, 334)-Net over F₉ — Digital

Digital (32, 54, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 27, 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]

(54−22, 54, 29668)-Net in Base 9 — Upper bound on s

There is no (32, 54, 29669)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3382 146713 168885 050279 483155 233761 781640 430389 260025 > 9⁵⁴ [i]