MinT - Best Known (112−50, 112, s)-Nets in Base 9

Best Known (112−50, 112, s)-Nets in Base 9

(112−50, 112, 320)-Net over F₉ — Constructive and digital

Digital (62, 112, 320)-net over F₉, using

2 times m-reduction [i] based on digital (62, 114, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 57, 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]

(112−50, 112, 380)-Net over F₉ — Digital

Digital (62, 112, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 56, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(112−50, 112, 23947)-Net in Base 9 — Upper bound on s

There is no (62, 112, 23948)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75022 068925 088301 917519 820016 781929 890838 645355 896938 756263 948033 195125 825481 320315 150114 259498 371016 290145 > 9¹¹² [i]