MinT - Best Known (194−51, 194, s)-Nets in Base 2

Best Known (194−51, 194, s)-Nets in Base 2

(194−51, 194, 144)-Net over F₂ — Constructive and digital

Digital (143, 194, 144)-net over F₂, using

4 times m-reduction [i] based on digital (143, 198, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 66, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(194−51, 194, 240)-Net over F₂ — Digital

Digital (143, 194, 240)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−51, 194, 2109)-Net in Base 2 — Upper bound on s

There is no (143, 194, 2110)-net in base 2, because

1 times m-reduction [i] would yield (143, 193, 2110)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12696 837439 203922 554095 949784 925739 653619 713707 978799 067391 > 2¹⁹³ [i]