MinT - Best Known (145−48, 145, s)-Nets in Base 3

Best Known (145−48, 145, s)-Nets in Base 3

(145−48, 145, 156)-Net over F₃ — Constructive and digital

Digital (97, 145, 156)-net over F₃, using

5 times m-reduction [i] based on digital (97, 150, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 75, 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]

(145−48, 145, 249)-Net over F₃ — Digital

Digital (97, 145, 249)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−48, 145, 3717)-Net in Base 3 — Upper bound on s

There is no (97, 145, 3718)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1530 878936 121134 122352 147079 674644 049039 025161 621012 763901 480485 796977 > 3¹⁴⁵ [i]