MinT - Best Known (141, 141+81, s)-Nets in Base 3

Best Known (141, 141+81, s)-Nets in Base 3

(141, 141+81, 156)-Net over F₃ — Constructive and digital

Digital (141, 222, 156)-net over F₃, using

16 times m-reduction [i] based on digital (141, 238, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 119, 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]

(141, 141+81, 266)-Net over F₃ — Digital

Digital (141, 222, 266)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+81, 3371)-Net in Base 3 — Upper bound on s

There is no (141, 222, 3372)-net in base 3, because

1 times m-reduction [i] would yield (141, 221, 3372)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2795 139424 231418 419200 033549 206102 990221 228109 251078 796411 574120 330080 921695 239150 269493 910913 716140 292801 > 3²²¹ [i]