MinT - Best Known (52−22, 52, s)-Nets in Base 9

Best Known (52−22, 52, s)-Nets in Base 9

(52−22, 52, 300)-Net over F₉ — Constructive and digital

Digital (30, 52, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 26, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(52−22, 52, 308)-Net over F₉ — Digital

Digital (30, 52, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 26, 154)-net over F₈₁, using
- net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
    - a curve from the manYPoints database [i]

(52−22, 52, 19895)-Net in Base 9 — Upper bound on s

There is no (30, 52, 19896)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41 762639 536403 363304 230114 970112 732001 166600 065089 > 9⁵² [i]