MinT - Best Known (132−33, 132, s)-Nets in Base 2

Best Known (132−33, 132, s)-Nets in Base 2

(132−33, 132, 144)-Net over F₂ — Constructive and digital

Digital (99, 132, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 44, 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]

(132−33, 132, 200)-Net over F₂ — Digital

Digital (99, 132, 200)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−33, 132, 1959)-Net in Base 2 — Upper bound on s

There is no (99, 132, 1960)-net in base 2, because

1 times m-reduction [i] would yield (99, 131, 1960)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2740 664955 956792 811179 040970 825819 322790 > 2¹³¹ [i]