MinT - Best Known (236−53, 236, s)-Nets in Base 3

Best Known (236−53, 236, s)-Nets in Base 3

(236−53, 236, 640)-Net over F₃ — Constructive and digital

Digital (183, 236, 640)-net over F₃, using

t-expansion [i] based on digital (182, 236, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 59, 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]

(236−53, 236, 1506)-Net over F₃ — Digital

Digital (183, 236, 1506)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−53, 236, 108293)-Net in Base 3 — Upper bound on s

There is no (183, 236, 108294)-net in base 3, because

1 times m-reduction [i] would yield (183, 235, 108294)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13290 257999 429110 345234 090852 294907 204582 734321 167068 564117 864079 408131 461981 356254 632788 447493 082646 705994 529565 > 3²³⁵ [i]