MinT - Best Known (239−94, 239, s)-Nets in Base 3

Best Known (239−94, 239, s)-Nets in Base 3

(239−94, 239, 156)-Net over F₃ — Constructive and digital

Digital (145, 239, 156)-net over F₃, using

7 times m-reduction [i] based on digital (145, 246, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 123, 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]

(239−94, 239, 229)-Net over F₃ — Digital

Digital (145, 239, 229)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−94, 239, 2404)-Net in Base 3 — Upper bound on s

There is no (145, 239, 2405)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 086444 986069 006365 612059 493460 953519 221607 152548 438598 072256 397124 903982 122364 592747 437588 111126 945272 217463 173755 > 3²³⁹ [i]