MinT - Best Known (211−79, 211, s)-Nets in Base 3

Best Known (211−79, 211, s)-Nets in Base 3

(211−79, 211, 156)-Net over F₃ — Constructive and digital

Digital (132, 211, 156)-net over F₃, using

9 times m-reduction [i] based on digital (132, 220, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 110, 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]

(211−79, 211, 237)-Net over F₃ — Digital

Digital (132, 211, 237)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−79, 211, 2816)-Net in Base 3 — Upper bound on s

There is no (132, 211, 2817)-net in base 3, because

1 times m-reduction [i] would yield (132, 210, 2817)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15882 281507 245330 429801 010006 267435 975773 806962 227650 360977 872818 513179 207285 342001 138296 635555 259403 > 3²¹⁰ [i]