MinT - Best Known (180, 180+53, s)-Nets in Base 3

Best Known (180, 180+53, s)-Nets in Base 3

(180, 180+53, 640)-Net over F₃ — Constructive and digital

Digital (180, 233, 640)-net over F₃, using

3¹ times duplication [i] based on digital (179, 232, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 58, 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]

(180, 180+53, 1415)-Net over F₃ — Digital

Digital (180, 233, 1415)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+53, 95397)-Net in Base 3 — Upper bound on s

There is no (180, 233, 95398)-net in base 3, because

1 times m-reduction [i] would yield (180, 232, 95398)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 492 265512 666101 674982 981896 226850 208750 177910 891685 776527 735289 014637 764813 414586 808241 751910 524029 561836 701661 > 3²³² [i]