MinT - Best Known (55−23, 55, s)-Nets in Base 2

Best Known (55−23, 55, s)-Nets in Base 2

(55−23, 55, 30)-Net over F₂ — Constructive and digital

Digital (32, 55, 30)-net over F₂, using

1 times m-reduction [i] based on digital (32, 56, 30)-net over F₂, using
- trace code for nets [i] based on digital (4, 28, 15)-net over F₄, using
  - net from sequence [i] based on digital (4, 14)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
      - an explicitly constructive algebraic function field [i]

(55−23, 55, 32)-Net over F₂ — Digital

Digital (32, 55, 32)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−23, 55, 132)-Net in Base 2 — Upper bound on s

There is no (32, 55, 133)-net in base 2, because

1 times m-reduction [i] would yield (32, 54, 133)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 19067 232255 261952 > 2⁵⁴ [i]