MinT - Best Known (116−52, 116, s)-Nets in Base 9

Best Known (116−52, 116, s)-Nets in Base 9

(116−52, 116, 320)-Net over F₉ — Constructive and digital

Digital (64, 116, 320)-net over F₉, using

2 times m-reduction [i] based on digital (64, 118, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 59, 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]

(116−52, 116, 380)-Net over F₉ — Digital

Digital (64, 116, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 58, 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]

(116−52, 116, 23839)-Net in Base 9 — Upper bound on s

There is no (64, 116, 23840)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 197175 684925 531155 989828 399121 171052 573882 119327 052500 159828 008173 994779 586559 859015 469092 356765 770608 696833 > 9¹¹⁶ [i]