MinT - Best Known (224−84, 224, s)-Nets in Base 3

Best Known (224−84, 224, s)-Nets in Base 3

(224−84, 224, 156)-Net over F₃ — Constructive and digital

Digital (140, 224, 156)-net over F₃, using

12 times m-reduction [i] based on digital (140, 236, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 118, 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]

(224−84, 224, 248)-Net over F₃ — Digital

Digital (140, 224, 248)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−84, 224, 2852)-Net in Base 3 — Upper bound on s

There is no (140, 224, 2853)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75878 305414 772654 232896 263444 654280 502081 860077 869180 140268 457724 958394 901125 848933 095594 042203 349400 007089 > 3²²⁴ [i]