MinT - Best Known (152−59, 152, s)-Nets in Base 2

Best Known (152−59, 152, s)-Nets in Base 2

(152−59, 152, 66)-Net over F₂ — Constructive and digital

Digital (93, 152, 66)-net over F₂, using

4 times m-reduction [i] based on digital (93, 156, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 78, 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]

(152−59, 152, 80)-Net over F₂ — Digital

Digital (93, 152, 80)-net over F₂, using

trace code for nets [i] based on digital (17, 76, 40)-net over F₄, using
- net from sequence [i] based on digital (17, 39)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 17 and N(F) ≥ 40, using
    - Drinfeld modules of rank 1 [i]

(152−59, 152, 389)-Net in Base 2 — Upper bound on s

There is no (93, 152, 390)-net in base 2, because

1 times m-reduction [i] would yield (93, 151, 390)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2867 313564 035361 123060 187831 081743 311961 285232 > 2¹⁵¹ [i]