MinT - Best Known (234−103, 234, s)-Nets in Base 2

Best Known (234−103, 234, s)-Nets in Base 2

(234−103, 234, 66)-Net over F₂ — Constructive and digital

Digital (131, 234, 66)-net over F₂, using

3 times m-reduction [i] based on digital (131, 237, 66)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 92, 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, 145, 33)-net over F₂, using
    - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(234−103, 234, 85)-Net over F₂ — Digital

Digital (131, 234, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−103, 234, 400)-Net in Base 2 — Upper bound on s

There is no (131, 234, 401)-net in base 2, because

1 times m-reduction [i] would yield (131, 233, 401)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14904 576056 489939 813483 273326 599295 405825 163266 119011 567607 949519 159136 > 2²³³ [i]