MinT - Best Known (186−43, 186, s)-Nets in Base 2

Best Known (186−43, 186, s)-Nets in Base 2

(186−43, 186, 195)-Net over F₂ — Constructive and digital

Digital (143, 186, 195)-net over F₂, using

t-expansion [i] based on digital (142, 186, 195)-net over F₂, using
- 6 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]

(186−43, 186, 323)-Net over F₂ — Digital

Digital (143, 186, 323)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−43, 186, 3863)-Net in Base 2 — Upper bound on s

There is no (143, 186, 3864)-net in base 2, because

1 times m-reduction [i] would yield (143, 185, 3864)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 49 209674 661912 556968 492064 788490 045153 496525 894238 505235 > 2¹⁸⁵ [i]