MinT - Best Known (189−73, 189, s)-Nets in Base 3

Best Known (189−73, 189, s)-Nets in Base 3

(189−73, 189, 148)-Net over F₃ — Constructive and digital

Digital (116, 189, 148)-net over F₃, using

9 times m-reduction [i] based on digital (116, 198, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 99, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(189−73, 189, 197)-Net over F₃ — Digital

Digital (116, 189, 197)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−73, 189, 2179)-Net in Base 3 — Upper bound on s

There is no (116, 189, 2180)-net in base 3, because

1 times m-reduction [i] would yield (116, 188, 2180)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 503345 103723 654618 421316 334484 178649 615091 013780 877426 693510 590584 798996 943719 310789 406913 > 3¹⁸⁸ [i]