  We optimize a silica-encapsulated silicon L3 photonic crystal cavity for
ultra-high quality factor by means of a global optimization strategy, where the
closest holes surrounding the cavity are varied to minimize out-of-plane
losses. We find an optimal value of $Q_c=4.33\times10^7$, thus setting a new
record for encapsulated low-index-contrast photonic crystal cavities. We also
address the effects of structural imperfections on our optimal cavity design
and predict an averaged $Q_c$ in the 2 million regime for state-of-the-art
silicon fabrication tolerances.
