MinT - Best Known (187−41, 187, s)-Nets in Base 3

Best Known (187−41, 187, s)-Nets in Base 3

(187−41, 187, 640)-Net over F₃ — Constructive and digital

Digital (146, 187, 640)-net over F₃, using

1 times m-reduction [i] based on digital (146, 188, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 47, 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]

(187−41, 187, 1360)-Net over F₃ — Digital

Digital (146, 187, 1360)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−41, 187, 113613)-Net in Base 3 — Upper bound on s

There is no (146, 187, 113614)-net in base 3, because

1 times m-reduction [i] would yield (146, 186, 113614)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55539 614270 187268 605434 316479 727323 742862 754087 883330 710464 584719 832582 230096 918479 812009 > 3¹⁸⁶ [i]