MinT - Best Known (56−37, 56, s)-Nets in Base 2

Best Known (56−37, 56, s)-Nets in Base 2

(56−37, 56, 20)-Net over F₂ — Constructive and digital

Digital (19, 56, 20)-net over F₂, using

net from sequence [i] based on digital (19, 19)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
  - an explicitly constructive algebraic function field [i]

(56−37, 56, 40)-Net in Base 2 — Upper bound on s

There is no (19, 56, 41)-net in base 2, because

1 times m-reduction [i] would yield (19, 55, 41)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 42100 907861 024624 > 2⁵⁵ [i]