MinT - Best Known (109−80, 109, s)-Nets in Base 9

Best Known (109−80, 109, s)-Nets in Base 9

(109−80, 109, 78)-Net over F₉ — Constructive and digital

Digital (29, 109, 78)-net over F₉, using

t-expansion [i] based on digital (22, 109, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(109−80, 109, 110)-Net over F₉ — Digital

Digital (29, 109, 110)-net over F₉, using

t-expansion [i] based on digital (26, 109, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(109−80, 109, 760)-Net in Base 9 — Upper bound on s

There is no (29, 109, 761)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 103 014051 632081 988206 094105 269123 151179 765445 345864 926721 357235 494270 830568 860081 279272 474366 170685 457985 > 9¹⁰⁹ [i]