MinT - Best Known (237−55, 237, s)-Nets in Base 3

Best Known (237−55, 237, s)-Nets in Base 3

(237−55, 237, 600)-Net over F₃ — Constructive and digital

Digital (182, 237, 600)-net over F₃, using

3¹ times duplication [i] based on digital (181, 236, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 59, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(237−55, 237, 1325)-Net over F₃ — Digital

Digital (182, 237, 1325)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−55, 237, 80840)-Net in Base 3 — Upper bound on s

There is no (182, 237, 80841)-net in base 3, because

1 times m-reduction [i] would yield (182, 236, 80841)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39877 234313 098770 045754 179014 904565 611415 128129 115906 401100 484156 824845 056576 014391 685454 855125 985240 237274 694171 > 3²³⁶ [i]