MinT - Best Known (52−19, 52, s)-Nets in Base 2

Best Known (52−19, 52, s)-Nets in Base 2

(52−19, 52, 42)-Net over F₂ — Constructive and digital

Digital (33, 52, 42)-net over F₂, using

trace code for nets [i] based on digital (7, 26, 21)-net over F₄, using
- net from sequence [i] based on digital (7, 20)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(52−19, 52, 198)-Net in Base 2 — Upper bound on s

There is no (33, 52, 199)-net in base 2, because

1 times m-reduction [i] would yield (33, 51, 199)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2349 036768 797472 > 2⁵¹ [i]