MinT - Best Known (55, 55+21, s)-Nets in Base 2

Best Known (55, 55+21, s)-Nets in Base 2

(55, 55+21, 75)-Net over F₂ — Constructive and digital

Digital (55, 76, 75)-net over F₂, using

2¹ times duplication [i] based on digital (54, 75, 75)-net over F₂, using
- trace code for nets [i] based on digital (4, 25, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]

(55, 55+21, 103)-Net over F₂ — Digital

Digital (55, 76, 103)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+21, 805)-Net in Base 2 — Upper bound on s

There is no (55, 76, 806)-net in base 2, because

1 times m-reduction [i] would yield (55, 75, 806)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 38055 819032 386255 322808 > 2⁷⁵ [i]