MinT - Best Known (205−45, 205, s)-Nets in Base 3

Best Known (205−45, 205, s)-Nets in Base 3

(205−45, 205, 640)-Net over F₃ — Constructive and digital

Digital (160, 205, 640)-net over F₃, using

3¹ times duplication [i] based on digital (159, 204, 640)-net over F₃, using
- t-expansion [i] based on digital (158, 204, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 51, 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]

(205−45, 205, 1463)-Net over F₃ — Digital

Digital (160, 205, 1463)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−45, 205, 120215)-Net in Base 3 — Upper bound on s

There is no (160, 205, 120216)-net in base 3, because

1 times m-reduction [i] would yield (160, 204, 120216)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 516509 258430 448030 091576 310296 187730 279766 475610 985618 178782 843954 052886 913972 082667 649214 743697 > 3²⁰⁴ [i]