MinT - Best Known (136, 136+74, s)-Nets in Base 3

Best Known (136, 136+74, s)-Nets in Base 3

(136, 136+74, 156)-Net over F₃ — Constructive and digital

Digital (136, 210, 156)-net over F₃, using

18 times m-reduction [i] based on digital (136, 228, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 114, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(136, 136+74, 281)-Net over F₃ — Digital

Digital (136, 210, 281)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+74, 3703)-Net in Base 3 — Upper bound on s

There is no (136, 210, 3704)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15744 712161 338033 282786 613145 302772 964179 890724 048429 764095 334783 635102 885986 580042 679319 436674 791537 > 3²¹⁰ [i]