MinT - Best Known (186, 237, s)-Nets in Base 3

Best Known (186, 237, s)-Nets in Base 3

(186, 237, 688)-Net over F₃ — Constructive and digital

Digital (186, 237, 688)-net over F₃, using

3¹ times duplication [i] based on 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]

(186, 237, 1804)-Net over F₃ — Digital

Digital (186, 237, 1804)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 237, 162388)-Net in Base 3 — Upper bound on s

There is no (186, 237, 162389)-net in base 3, because

1 times m-reduction [i] would yield (186, 236, 162389)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39871 010827 323088 153519 065799 776221 433134 983275 869938 752146 089932 146449 938950 119643 257716 888307 283738 582534 510283 > 3²³⁶ [i]