MinT - Best Known (150−55, 150, s)-Nets in Base 2

Best Known (150−55, 150, s)-Nets in Base 2

(150−55, 150, 66)-Net over F₂ — Constructive and digital

Digital (95, 150, 66)-net over F₂, using

10 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]

(150−55, 150, 89)-Net over F₂ — Digital

Digital (95, 150, 89)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−55, 150, 462)-Net in Base 2 — Upper bound on s

There is no (95, 150, 463)-net in base 2, because

1 times m-reduction [i] would yield (95, 149, 463)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 746 070925 341544 027234 850469 415760 656713 482200 > 2¹⁴⁹ [i]