MinT - Best Known (141, 141+51, s)-Nets in Base 2

Best Known (141, 141+51, s)-Nets in Base 2

(141, 141+51, 144)-Net over F₂ — Constructive and digital

Digital (141, 192, 144)-net over F₂, using

3 times m-reduction [i] based on digital (141, 195, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 65, 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]

(141, 141+51, 231)-Net over F₂ — Digital

Digital (141, 192, 231)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+51, 1993)-Net in Base 2 — Upper bound on s

There is no (141, 192, 1994)-net in base 2, because

1 times m-reduction [i] would yield (141, 191, 1994)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3165 715671 449937 249931 143468 363254 722994 889490 995118 980276 > 2¹⁹¹ [i]