  We give a conditional result on the constant in the B\'aez-Duarte
reformulation of the Nyman-Beurling criterion for the Riemann Hypothesis. We
show that assuming the Riemann hypothesis and that
$\sum_{\rho}\frac{1}{|\zeta'(\rho)|^2}\ll T^{3/2-\delta}$, for some $\delta>0$,
the value of this constant coincides with the lower bound given by Burnol.
