MinT - Best Known (137, 137+49, s)-Nets in Base 2

Best Known (137, 137+49, s)-Nets in Base 2

(137, 137+49, 144)-Net over F₂ — Constructive and digital

Digital (137, 186, 144)-net over F₂, using

3 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]

(137, 137+49, 230)-Net over F₂ — Digital

Digital (137, 186, 230)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+49, 2015)-Net in Base 2 — Upper bound on s

There is no (137, 186, 2016)-net in base 2, because

1 times m-reduction [i] would yield (137, 185, 2016)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 49 613351 139631 144955 902679 322716 156309 863668 880441 685627 > 2¹⁸⁵ [i]