MinT - Best Known (142, 142+42, s)-Nets in Base 2

Best Known (142, 142+42, s)-Nets in Base 2

(142, 142+42, 195)-Net over F₂ — Constructive and digital

Digital (142, 184, 195)-net over F₂, using

8 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]

(142, 142+42, 331)-Net over F₂ — Digital

Digital (142, 184, 331)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+42, 3736)-Net in Base 2 — Upper bound on s

There is no (142, 184, 3737)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 24 530400 094550 484197 247474 105085 830203 643269 347918 724092 > 2¹⁸⁴ [i]