MinT - Best Known (136, 224, s)-Nets in Base 3

Best Known (136, 224, s)-Nets in Base 3

(136, 224, 156)-Net over F₃ — Constructive and digital

Digital (136, 224, 156)-net over F₃, using

4 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, 224, 217)-Net over F₃ — Digital

Digital (136, 224, 217)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 224, 2273)-Net in Base 3 — Upper bound on s

There is no (136, 224, 2274)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75649 711664 650776 357624 349590 345783 163868 154736 797855 906772 752603 696026 004071 399336 551529 908053 302346 878649 > 3²²⁴ [i]