MinT - Best Known (156−52, 156, s)-Nets in Base 3

Best Known (156−52, 156, s)-Nets in Base 3

(156−52, 156, 156)-Net over F₃ — Constructive and digital

Digital (104, 156, 156)-net over F₃, using

8 times m-reduction [i] based on digital (104, 164, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 82, 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]

(156−52, 156, 259)-Net over F₃ — Digital

Digital (104, 156, 259)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−52, 156, 3820)-Net in Base 3 — Upper bound on s

There is no (104, 156, 3821)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 270 809122 931077 585260 341512 561733 913181 305659 125021 384218 813618 560640 624321 > 3¹⁵⁶ [i]