MinT - Best Known (96−43, 96, s)-Nets in Base 9

Best Known (96−43, 96, s)-Nets in Base 9

(96−43, 96, 320)-Net over F₉ — Constructive and digital

Digital (53, 96, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 48, 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]

(96−43, 96, 334)-Net over F₉ — Digital

Digital (53, 96, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 48, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(96−43, 96, 22489)-Net in Base 9 — Upper bound on s

There is no (53, 96, 22490)-net in base 9, because

1 times m-reduction [i] would yield (53, 95, 22490)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 502376 335153 085537 513682 880348 864683 062961 522862 243428 847048 494362 459249 290153 205148 218001 > 9⁹⁵ [i]