MinT - Best Known (144, 144+97, s)-Nets in Base 2

Best Known (144, 144+97, s)-Nets in Base 2

(144, 144+97, 75)-Net over F₂ — Constructive and digital

Digital (144, 241, 75)-net over F₂, using

5 times m-reduction [i] based on digital (144, 246, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 90, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
        an explicitly constructive algebraic function field [i]
  2. digital (54, 156, 42)-net over F₂, using
    - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
        an explicitly constructive algebraic function field [i]

(144, 144+97, 107)-Net over F₂ — Digital

Digital (144, 241, 107)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+97, 531)-Net in Base 2 — Upper bound on s

There is no (144, 241, 532)-net in base 2, because

1 times m-reduction [i] would yield (144, 240, 532)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 785118 918408 658125 709489 662472 321625 316060 482517 841864 559446 783686 527120 > 2²⁴⁰ [i]