MinT - Best Known (189−47, 189, s)-Nets in Base 2

Best Known (189−47, 189, s)-Nets in Base 2

(189−47, 189, 195)-Net over F₂ — Constructive and digital

Digital (142, 189, 195)-net over F₂, using

3 times m-reduction [i] based on digital (142, 192, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 64, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(189−47, 189, 271)-Net over F₂ — Digital

Digital (142, 189, 271)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−47, 189, 2689)-Net in Base 2 — Upper bound on s

There is no (142, 189, 2690)-net in base 2, because

1 times m-reduction [i] would yield (142, 188, 2690)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 394 969249 336742 579219 962913 124855 794881 528890 824723 648704 > 2¹⁸⁸ [i]