Theoretical-computational studies of table-top laser-driven nuclear fusion of high energy (up to 15 MeV) deuterons with 7Li, 6Li, T, and D demonstrate the attainment of high fusion yields. The reaction design constitutes a source of Coulomb exploding deuterium nanodroplets driven by an ultraintense, near-infrared, femtosecond Gaussian laser pulse (peak intensity 2 × 1018-5 × 1019 W cm-2) and a solid, hollow cylindrical target containing the second reagent. The exploding nanodroplets source is characterized by the deuteron kinetic energies, their number, and the laser energy absorbed by a nanodroplet. These were computed by scaled electron and ion dynamics simulations, which account for intra-nanodroplet laser intensity attenuation and relativistic effects. The fusion yields Y are determined by the number of the source deuterons and by the reaction probability. When laser intensity attenuation is weak within a single nanodroplet and throughout the nanodroplets assembly, Y exhibits a power law increase with increasing the nanodroplet size. Y is maximized for the nanodroplet size and laser intensity corresponding to the "transition" between the weak and the strong intensity attenuation domains. The dependence of Y on the laser pulse energy W scales as W2 for weak assembly intensity attenuation, and as W for strong assembly intensity attenuation. This reaction design attains the highest table-top fusion efficiencies (up to 4 × 109 J-1 per laser pulse) obtained up to date.