MinT - Best Known (96−44, 96, s)-Nets in Base 9

Best Known (96−44, 96, s)-Nets in Base 9

(96−44, 96, 300)-Net over F₉ — Constructive and digital

Digital (52, 96, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 48, 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]

(96−44, 96, 308)-Net over F₉ — Digital

Digital (52, 96, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 48, 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]

(96−44, 96, 16496)-Net in Base 9 — Upper bound on s

There is no (52, 96, 16497)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 40 531396 338381 228770 934104 633606 749709 513972 036748 172365 218676 366613 920280 035903 435977 983345 > 9⁹⁶ [i]