MinT - Best Known (243−96, 243, s)-Nets in Base 3

Best Known (243−96, 243, s)-Nets in Base 3

(243−96, 243, 156)-Net over F₃ — Constructive and digital

Digital (147, 243, 156)-net over F₃, using

7 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 125, 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]

(243−96, 243, 229)-Net over F₃ — Digital

Digital (147, 243, 229)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−96, 243, 2391)-Net in Base 3 — Upper bound on s

There is no (147, 243, 2392)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 640876 436440 102083 509696 723915 347341 224383 953345 679608 153951 359115 411090 645208 215212 688388 622281 637497 729078 765569 > 3²⁴³ [i]