Moduli stabilization in type IIB orientifolds at $h^{2,1}=50$

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 $N_{\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{x}}$. Based on recent results by Crinò et al. we estimate the bound imposed by the tadpole-cancellation condition as $N_{\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{x}}\le \mathcal{O}({10}^3)$, however, the smallest flux number we obtain in our search is of order $N_{\mathrm{f}\mathrm{l}\mathrm{u}\mathrm{x}}=\mathcal{O}({10}^4)$. This implies, in particular, that for all solutions to the F-term equations in our data set the tadpole conjecture is satisfied.