MinT - Best Known (135, 135+49, s)-Nets in Base 2

Best Known (135, 135+49, s)-Nets in Base 2

(135, 135+49, 144)-Net over F₂ — Constructive and digital

Digital (135, 184, 144)-net over F₂, using

2 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]

(135, 135+49, 222)-Net over F₂ — Digital

Digital (135, 184, 222)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+49, 1899)-Net in Base 2 — Upper bound on s

There is no (135, 184, 1900)-net in base 2, because

1 times m-reduction [i] would yield (135, 183, 1900)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12 267182 453975 277356 935269 201915 480134 067842 055578 404046 > 2¹⁸³ [i]