MinT - Best Known (236−51, 236, s)-Nets in Base 3

Best Known (236−51, 236, s)-Nets in Base 3

(236−51, 236, 688)-Net over F₃ — Constructive and digital

Digital (185, 236, 688)-net over F₃, using

t-expansion [i] based on digital (184, 236, 688)-net over F₃, using
- trace code for nets [i] based on digital (7, 59, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(236−51, 236, 1765)-Net over F₃ — Digital

Digital (185, 236, 1765)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−51, 236, 155405)-Net in Base 3 — Upper bound on s

There is no (185, 236, 155406)-net in base 3, because

1 times m-reduction [i] would yield (185, 235, 155406)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13289 547750 119299 584131 046272 181764 183674 484837 896745 725081 695691 163980 929770 370305 351600 727403 482784 112552 623725 > 3²³⁵ [i]