MinT - Best Known (247−56, 247, s)-Nets in Base 3

Best Known (247−56, 247, s)-Nets in Base 3

(247−56, 247, 640)-Net over F₃ — Constructive and digital

Digital (191, 247, 640)-net over F₃, using

1 times m-reduction [i] based on digital (191, 248, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 62, 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]

(247−56, 247, 1509)-Net over F₃ — Digital

Digital (191, 247, 1509)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−56, 247, 91355)-Net in Base 3 — Upper bound on s

There is no (191, 247, 91356)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7063 121028 995147 143773 988923 115089 779968 446884 037120 941589 185450 356732 974312 102864 744811 833804 419760 356404 283252 438977 > 3²⁴⁷ [i]