MinT - Best Known (195, 195+47, s)-Nets in Base 3

Best Known (195, 195+47, s)-Nets in Base 3

(195, 195+47, 896)-Net over F₃ — Constructive and digital

Digital (195, 242, 896)-net over F₃, using

3² times duplication [i] based on digital (193, 240, 896)-net over F₃, using
- trace code for nets [i] based on digital (13, 60, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(195, 195+47, 2935)-Net over F₃ — Digital

Digital (195, 242, 2935)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(195, 195+47, 470767)-Net in Base 3 — Upper bound on s

There is no (195, 242, 470768)-net in base 3, because

1 times m-reduction [i] would yield (195, 241, 470768)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 687960 257035 131090 293421 225232 226491 723656 002159 662640 108738 733194 502843 918896 158428 226319 547338 742502 051641 518913 > 3²⁴¹ [i]