MinT - Best Known (174−67, 174, s)-Nets in Base 2

Best Known (174−67, 174, s)-Nets in Base 2

(174−67, 174, 66)-Net over F₂ — Constructive and digital

Digital (107, 174, 66)-net over F₂, using

10 times m-reduction [i] based on digital (107, 184, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 92, 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]

(174−67, 174, 90)-Net over F₂ — Digital

Digital (107, 174, 90)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−67, 174, 451)-Net in Base 2 — Upper bound on s

There is no (107, 174, 452)-net in base 2, because

1 times m-reduction [i] would yield (107, 173, 452)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12477 118029 801395 740481 288899 036708 342824 278436 480450 > 2¹⁷³ [i]