MinT - Best Known (56, 56+85, s)-Nets in Base 2

Best Known (56, 56+85, s)-Nets in Base 2

(56, 56+85, 42)-Net over F₂ — Constructive and digital

Digital (56, 141, 42)-net over F₂, using

t-expansion [i] based on digital (54, 141, 42)-net over F₂, using
- net from sequence [i] based on digital (54, 41)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(56, 56+85, 112)-Net in Base 2 — Upper bound on s

There is no (56, 141, 113)-net in base 2, because

1 times m-reduction [i] would yield (56, 140, 113)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 433999 729955 892848 531054 277899 318868 796544 > 2¹⁴⁰ [i]