MinT - Best Known (163, 163+47, s)-Nets in Base 3

Best Known (163, 163+47, s)-Nets in Base 3

(163, 163+47, 640)-Net over F₃ — Constructive and digital

Digital (163, 210, 640)-net over F₃, using

3² times duplication [i] based on digital (161, 208, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 52, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(163, 163+47, 1379)-Net over F₃ — Digital

Digital (163, 210, 1379)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+47, 102072)-Net in Base 3 — Upper bound on s

There is no (163, 210, 102073)-net in base 3, because

1 times m-reduction [i] would yield (163, 209, 102073)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5228 138423 001466 475292 156395 265043 609849 421682 325168 911659 012496 264022 927321 442931 975723 394821 045291 > 3²⁰⁹ [i]