MinT - Best Known (193−50, 193, s)-Nets in Base 2

Best Known (193−50, 193, s)-Nets in Base 2

(193−50, 193, 195)-Net over F₂ — Constructive and digital

Digital (143, 193, 195)-net over F₂, using

2¹ times duplication [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]

(193−50, 193, 248)-Net over F₂ — Digital

Digital (143, 193, 248)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−50, 193, 2109)-Net in Base 2 — Upper bound on s

There is no (143, 193, 2110)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12696 837439 203922 554095 949784 925739 653619 713707 978799 067391 > 2¹⁹³ [i]