MinT - Best Known (114−52, 114, s)-Nets in Base 9

Best Known (114−52, 114, s)-Nets in Base 9

(114−52, 114, 320)-Net over F₉ — Constructive and digital

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]

(114−52, 114, 334)-Net over F₉ — Digital

Digital (62, 114, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 57, 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]

(114−52, 114, 20130)-Net in Base 9 — Upper bound on s

There is no (62, 114, 20131)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 082029 360757 296005 412166 667804 018879 095372 270086 363060 873680 348902 707310 272654 773102 973587 430848 185421 531121 > 9¹¹⁴ [i]