MinT - Best Known (129−42, 129, s)-Nets in Base 3

Best Known (129−42, 129, s)-Nets in Base 3

(129−42, 129, 156)-Net over F₃ — Constructive and digital

Digital (87, 129, 156)-net over F₃, using

1 times m-reduction [i] based on digital (87, 130, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 65, 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]

(129−42, 129, 237)-Net over F₃ — Digital

Digital (87, 129, 237)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−42, 129, 3680)-Net in Base 3 — Upper bound on s

There is no (87, 129, 3681)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35 408060 288334 735323 041082 698363 078711 088933 554401 203816 896371 > 3¹²⁹ [i]