MinT - Best Known (54, 54+44, s)-Nets in Base 9

Best Known (54, 54+44, s)-Nets in Base 9

(54, 54+44, 320)-Net over F₉ — Constructive and digital

Digital (54, 98, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 49, 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, 54+44, 334)-Net over F₉ — Digital

Digital (54, 98, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 49, 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, 54+44, 20146)-Net in Base 9 — Upper bound on s

There is no (54, 98, 20147)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3281 874567 244831 923202 384276 014631 998038 089972 731554 275425 566608 479627 631901 018468 266580 192145 > 9⁹⁸ [i]