MinT - Best Known (186−45, 186, s)-Nets in Base 2

Best Known (186−45, 186, s)-Nets in Base 2

(186−45, 186, 195)-Net over F₂ — Constructive and digital

Digital (141, 186, 195)-net over F₂, using

t-expansion [i] based on digital (140, 186, 195)-net over F₂, using
- 3 times m-reduction [i] based on digital (140, 189, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 63, 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]

(186−45, 186, 288)-Net over F₂ — Digital

Digital (141, 186, 288)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−45, 186, 3045)-Net in Base 2 — Upper bound on s

There is no (141, 186, 3046)-net in base 2, because

1 times m-reduction [i] would yield (141, 185, 3046)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 49 227953 551733 244271 982430 504667 110970 899171 998898 610464 > 2¹⁸⁵ [i]