MinT - Best Known (169−62, 169, s)-Nets in Base 3

Best Known (169−62, 169, s)-Nets in Base 3

(169−62, 169, 156)-Net over F₃ — Constructive and digital

Digital (107, 169, 156)-net over F₃, using

1 times m-reduction [i] based on digital (107, 170, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 85, 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]

(169−62, 169, 207)-Net over F₃ — Digital

Digital (107, 169, 207)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−62, 169, 2447)-Net in Base 3 — Upper bound on s

There is no (107, 169, 2448)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 432 432704 364327 679906 102547 021365 062566 974838 356243 059963 197904 904315 754069 029569 > 3¹⁶⁹ [i]