MinT - Best Known (135, 182, s)-Nets in Base 2

Best Known (135, 182, s)-Nets in Base 2

(135, 182, 144)-Net over F₂ — Constructive and digital

Digital (135, 182, 144)-net over F₂, using

4 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, 182, 238)-Net over F₂ — Digital

Digital (135, 182, 238)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 182, 2171)-Net in Base 2 — Upper bound on s

There is no (135, 182, 2172)-net in base 2, because

1 times m-reduction [i] would yield (135, 181, 2172)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 085730 975691 934228 952065 770070 786634 689189 906104 966670 > 2¹⁸¹ [i]