MinT - Best Known (193−51, 193, s)-Nets in Base 2

Best Known (193−51, 193, s)-Nets in Base 2

(193−51, 193, 144)-Net over F₂ — Constructive and digital

Digital (142, 193, 144)-net over F₂, using

t-expansion [i] based on digital (141, 193, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (141, 195, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 65, 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]

(193−51, 193, 235)-Net over F₂ — Digital

Digital (142, 193, 235)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−51, 193, 2050)-Net in Base 2 — Upper bound on s

There is no (142, 193, 2051)-net in base 2, because

1 times m-reduction [i] would yield (142, 192, 2051)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6325 189745 134956 234704 551173 288251 750642 512878 522460 376064 > 2¹⁹² [i]