MinT - Best Known (159−64, 159, s)-Nets in Base 2

Best Known (159−64, 159, s)-Nets in Base 2

(159−64, 159, 66)-Net over F₂ — Constructive and digital

Digital (95, 159, 66)-net over F₂, using

1 times m-reduction [i] based on digital (95, 160, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 80, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(159−64, 159, 75)-Net over F₂ — Digital

Digital (95, 159, 75)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−64, 159, 355)-Net in Base 2 — Upper bound on s

There is no (95, 159, 356)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 764591 544801 481039 509153 652372 822806 943096 827447 > 2¹⁵⁹ [i]