MinT - Best Known (250−103, 250, s)-Nets in Base 2

Best Known (250−103, 250, s)-Nets in Base 2

(250−103, 250, 75)-Net over F₂ — Constructive and digital

Digital (147, 250, 75)-net over F₂, using

5 times m-reduction [i] based on digital (147, 255, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 93, 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, 162, 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]

(250−103, 250, 104)-Net over F₂ — Digital

Digital (147, 250, 104)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−103, 250, 513)-Net in Base 2 — Upper bound on s

There is no (147, 250, 514)-net in base 2, because

1 times m-reduction [i] would yield (147, 249, 514)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 920 368644 538862 986568 224936 313151 701782 305591 347174 267698 301326 017237 490560 > 2²⁴⁹ [i]