MinT - Best Known (112−52, 112, s)-Nets in Base 9

Best Known (112−52, 112, s)-Nets in Base 9

(112−52, 112, 300)-Net over F₉ — Constructive and digital

Digital (60, 112, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 56, 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]

(112−52, 112, 308)-Net over F₉ — Digital

Digital (60, 112, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 56, 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]

(112−52, 112, 16997)-Net in Base 9 — Upper bound on s

There is no (60, 112, 16998)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75079 086172 871385 007893 770952 131125 388840 093036 170227 940126 458045 634371 142443 103048 762323 698555 360691 562785 > 9¹¹² [i]