MinT - Best Known (163, 209, s)-Nets in Base 3

Best Known (163, 209, s)-Nets in Base 3

(163, 209, 640)-Net over F₃ — Constructive and digital

Digital (163, 209, 640)-net over F₃, using

3¹ times duplication [i] based on digital (162, 208, 640)-net over F₃, using
- t-expansion [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, 209, 1471)-Net over F₃ — Digital

Digital (163, 209, 1471)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 209, 102072)-Net in Base 3 — Upper bound on s

There is no (163, 209, 102073)-net in base 3, because

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]