MinT - Best Known (138, 187, s)-Nets in Base 2

Best Known (138, 187, s)-Nets in Base 2

(138, 187, 144)-Net over F₂ — Constructive and digital

Digital (138, 187, 144)-net over F₂, using

t-expansion [i] based on digital (137, 187, 144)-net over F₂, using
- 2 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, 187, 234)-Net over F₂ — Digital

Digital (138, 187, 234)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 187, 2075)-Net in Base 2 — Upper bound on s

There is no (138, 187, 2076)-net in base 2, because

1 times m-reduction [i] would yield (138, 186, 2076)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 99 116707 215350 814397 478807 098809 797473 203111 508725 949421 > 2¹⁸⁶ [i]