MinT - Best Known (241−97, 241, s)-Nets in Base 3

Best Known (241−97, 241, s)-Nets in Base 3

(241−97, 241, 156)-Net over F₃ — Constructive and digital

Digital (144, 241, 156)-net over F₃, using

3 times m-reduction [i] based on digital (144, 244, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 122, 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]

(241−97, 241, 216)-Net over F₃ — Digital

Digital (144, 241, 216)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−97, 241, 2229)-Net in Base 3 — Upper bound on s

There is no (144, 241, 2230)-net in base 3, because

1 times m-reduction [i] would yield (144, 240, 2230)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 234385 045460 049409 240935 976721 353933 417746 840364 717650 632477 115308 990707 729712 168610 320084 026529 266396 026432 312801 > 3²⁴⁰ [i]