MinT - Best Known (162, 162+57, s)-Nets in Base 2

Best Known (162, 162+57, s)-Nets in Base 2

(162, 162+57, 195)-Net over F₂ — Constructive and digital

Digital (162, 219, 195)-net over F₂, using

3 times m-reduction [i] based on digital (162, 222, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 74, 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]

(162, 162+57, 272)-Net over F₂ — Digital

Digital (162, 219, 272)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+57, 2451)-Net in Base 2 — Upper bound on s

There is no (162, 219, 2452)-net in base 2, because

1 times m-reduction [i] would yield (162, 218, 2452)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 421690 772771 833827 674673 610400 790591 609797 025342 941336 027150 591200 > 2²¹⁸ [i]