MinT - Best Known (185−43, 185, s)-Nets in Base 2

Best Known (185−43, 185, s)-Nets in Base 2

(185−43, 185, 195)-Net over F₂ — Constructive and digital

Digital (142, 185, 195)-net over F₂, using

7 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]

(185−43, 185, 317)-Net over F₂ — Digital

Digital (142, 185, 317)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−43, 185, 3736)-Net in Base 2 — Upper bound on s

There is no (142, 185, 3737)-net in base 2, because

1 times m-reduction [i] would yield (142, 184, 3737)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 24 530400 094550 484197 247474 105085 830203 643269 347918 724092 > 2¹⁸⁴ [i]