MinT - Best Known (214−85, 214, s)-Nets in Base 3

Best Known (214−85, 214, s)-Nets in Base 3

(214−85, 214, 156)-Net over F₃ — Constructive and digital

Digital (129, 214, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 107, 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]

(214−85, 214, 202)-Net over F₃ — Digital

Digital (129, 214, 202)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−85, 214, 2128)-Net in Base 3 — Upper bound on s

There is no (129, 214, 2129)-net in base 3, because

1 times m-reduction [i] would yield (129, 213, 2129)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 424949 851964 057090 549629 033559 960251 372479 400255 324117 425899 835626 066554 353772 998800 144141 976894 435657 > 3²¹³ [i]