MinT - Best Known (108, 108+63, s)-Nets in Base 3

Best Known (108, 108+63, s)-Nets in Base 3

(108, 108+63, 156)-Net over F₃ — Constructive and digital

Digital (108, 171, 156)-net over F₃, using

1 times m-reduction [i] based on digital (108, 172, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 86, 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]

(108, 108+63, 206)-Net over F₃ — Digital

Digital (108, 171, 206)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+63, 2536)-Net in Base 3 — Upper bound on s

There is no (108, 171, 2537)-net in base 3, because

1 times m-reduction [i] would yield (108, 170, 2537)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1291 050993 151210 882200 665616 414196 839042 632292 822596 879509 687760 114425 828181 424075 > 3¹⁷⁰ [i]