  We study moduli stabilization in Calabi-Yau orientifold compactifications of
type IIB string theory with O3- and O7-planes. We consider a Calabi-Yau
three-fold with Hodge number $h^{2,1}=50$ and stabilize all axio-dilaton and
complex-structure moduli by three-form fluxes. This is a challenging task,
especially for large moduli-space dimensions. To address this question we
develop an algorithm to generate $10^5$ flux vacua with small flux number
$N_{\rm flux}$. Based on recent results by Crin\`o et al. we estimate the bound
imposed by the tadpole-cancellation condition as $N_{\rm flux}\leq \mathcal
O(10^3)$, however, the smallest flux number we obtain in our search is of order
$N_{\rm flux}=\mathcal O(10^{4})$. This implies, in particular, that for all
solutions to the F-term equations in our data set the tadpole conjecture is
satisfied.
