MinT - Best Known (136, 136+49, s)-Nets in Base 2

Best Known (136, 136+49, s)-Nets in Base 2

(136, 136+49, 144)-Net over F₂ — Constructive and digital

Digital (136, 185, 144)-net over F₂, using

t-expansion [i] based on digital (135, 185, 144)-net over F₂, using
- 1 times m-reduction [i] based on digital (135, 186, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 62, 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]

(136, 136+49, 226)-Net over F₂ — Digital

Digital (136, 185, 226)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+49, 1956)-Net in Base 2 — Upper bound on s

There is no (136, 185, 1957)-net in base 2, because

1 times m-reduction [i] would yield (136, 184, 1957)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 24 623938 807171 557150 658546 486089 864488 925010 528738 092244 > 2¹⁸⁴ [i]