MinT - Best Known (41, 41+27, s)-Nets in Base 2

Best Known (41, 41+27, s)-Nets in Base 2

(41, 41+27, 42)-Net over F₂ — Constructive and digital

Digital (41, 68, 42)-net over F₂, using

trace code for nets [i] based on digital (7, 34, 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]

(41, 41+27, 183)-Net in Base 2 — Upper bound on s

There is no (41, 68, 184)-net in base 2, because

1 times m-reduction [i] would yield (41, 67, 184)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 151 980415 410067 319754 > 2⁶⁷ [i]