The work function and stability of 570 alloyed alkali-earth oxide films on W(100) have been calculated within density functional theory. Computational screening of this large phase space was enabled by utilizing the virtual crystal approximation, where the degree of freedom in the chemical composition is modeled with virtual atoms of mixed Ca, Sr, and Ba character. Low work functions are achieved by doping the films with Sc or Li and alloys containing small amounts of Ca. In particular, Li-doped systems with small Ca content also show favorable stability. Identification of such alloys outperforming any of the constituents relies on careful sampling of the chemical composition. We have identified the interactions within the film that limit the reduction in work function given by the dipole normal to the surface. We have shown that control of the screening of the intrafilm interactions by O atoms is essential for the design of new low work function materials.