MinT - Best Known (152−57, 152, s)-Nets in Base 2

Best Known (152−57, 152, s)-Nets in Base 2

(152−57, 152, 66)-Net over F₂ — Constructive and digital

Digital (95, 152, 66)-net over F₂, using

8 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]

(152−57, 152, 85)-Net over F₂ — Digital

Digital (95, 152, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−57, 152, 434)-Net in Base 2 — Upper bound on s

There is no (95, 152, 435)-net in base 2, because

1 times m-reduction [i] would yield (95, 151, 435)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2892 171677 172129 113317 003325 171899 945749 297624 > 2¹⁵¹ [i]