MinT - Best Known (232−102, 232, s)-Nets in Base 2

Best Known (232−102, 232, s)-Nets in Base 2

(232−102, 232, 66)-Net over F₂ — Constructive and digital

Digital (130, 232, 66)-net over F₂, using

2 times m-reduction [i] based on digital (130, 234, 66)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 91, 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 (39, 143, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(232−102, 232, 84)-Net over F₂ — Digital

Digital (130, 232, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−102, 232, 394)-Net in Base 2 — Upper bound on s

There is no (130, 232, 395)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7708 016625 700940 828776 386005 799759 449221 763131 746614 609993 499304 611824 > 2²³² [i]