MinT - Best Known (151−59, 151, s)-Nets in Base 2

Best Known (151−59, 151, s)-Nets in Base 2

(151−59, 151, 66)-Net over F₂ — Constructive and digital

Digital (92, 151, 66)-net over F₂, using

3 times m-reduction [i] based on digital (92, 154, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 77, 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]

(151−59, 151, 77)-Net over F₂ — Digital

Digital (92, 151, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−59, 151, 379)-Net in Base 2 — Upper bound on s

There is no (92, 151, 380)-net in base 2, because

1 times m-reduction [i] would yield (92, 150, 380)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1447 641798 145725 950032 863157 414699 961889 233312 > 2¹⁵⁰ [i]