MinT - Best Known (241−95, 241, s)-Nets in Base 3

Best Known (241−95, 241, s)-Nets in Base 3

(241−95, 241, 156)-Net over F₃ — Constructive and digital

Digital (146, 241, 156)-net over F₃, using

7 times m-reduction [i] based on digital (146, 248, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 124, 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]

(241−95, 241, 229)-Net over F₃ — Digital

Digital (146, 241, 229)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−95, 241, 2462)-Net in Base 3 — Upper bound on s

There is no (146, 241, 2463)-net in base 3, because

1 times m-reduction [i] would yield (146, 240, 2463)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 261706 482911 739959 094588 496063 504468 317165 032255 660968 830857 449962 084987 948975 809264 442108 429887 902683 389993 324067 > 3²⁴⁰ [i]