MinT - Best Known (138, 138+50, s)-Nets in Base 2

Best Known (138, 138+50, s)-Nets in Base 2

(138, 138+50, 144)-Net over F₂ — Constructive and digital

Digital (138, 188, 144)-net over F₂, using

t-expansion [i] based on digital (137, 188, 144)-net over F₂, using
- 1 times m-reduction [i] based on digital (137, 189, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 63, 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]

(138, 138+50, 227)-Net over F₂ — Digital

Digital (138, 188, 227)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+50, 1831)-Net in Base 2 — Upper bound on s

There is no (138, 188, 1832)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 395 970778 665133 521121 160605 869835 020409 114912 162368 909300 > 2¹⁸⁸ [i]