MinT - Best Known (57, 57+91, s)-Nets in Base 2

Best Known (57, 57+91, s)-Nets in Base 2

(57, 57+91, 42)-Net over F₂ — Constructive and digital

Digital (57, 148, 42)-net over F₂, using

t-expansion [i] based on digital (54, 148, 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]

(57, 57+91, 112)-Net in Base 2 — Upper bound on s

There is no (57, 148, 113)-net in base 2, because

1 times m-reduction [i] would yield (57, 147, 113)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 195 679118 911417 647351 693762 117787 125296 076744 > 2¹⁴⁷ [i]