MinT - Best Known (186, 241, s)-Nets in Base 3

Best Known (186, 241, s)-Nets in Base 3

(186, 241, 640)-Net over F₃ — Constructive and digital

Digital (186, 241, 640)-net over F₃, using

3¹ times duplication [i] based on digital (185, 240, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 60, 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]

(186, 241, 1439)-Net over F₃ — Digital

Digital (186, 241, 1439)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 241, 95133)-Net in Base 3 — Upper bound on s

There is no (186, 241, 95134)-net in base 3, because

1 times m-reduction [i] would yield (186, 240, 95134)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 229669 069725 118249 239571 179134 703791 560271 811985 854583 907611 841902 218173 290357 872982 013331 648223 094602 054824 050321 > 3²⁴⁰ [i]