MinT - Best Known (36, 64, s)-Nets in Base 9

Best Known (36, 64, s)-Nets in Base 9

(36, 64, 300)-Net over F₉ — Constructive and digital

Digital (36, 64, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 32, 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]

(36, 64, 308)-Net over F₉ — Digital

Digital (36, 64, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 32, 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]

(36, 64, 17394)-Net in Base 9 — Upper bound on s

There is no (36, 64, 17395)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 794405 930751 095706 465825 528454 865061 641603 129079 752963 066065 > 9⁶⁴ [i]