We use hexagonal mesophases made of oil-swollen surfactant-stabilized tubes arranged on a triangular lattice in water and doped with metallic salts as templates for the radiolytic synthesis of nanostructures. The nanostructures formed in this type of soft matrix are bimetallic palladium-platinum porous nanoballs composed of 3D-connected nanowires, of typical thickness 2.5 nm, forming hexagonal cells. We demonstrate using electron microscopy and small-angle X-ray scattering that the pore size of the nanoballs is directly determined by the diameter of the oil tube of the doped mesophases, which we have varied in a controlled fashion from 10 to 55 nm. Bimetallic nanostructures comprising various proportions of palladium and platinum can be synthesized. Their alloy structure was evidenced by X-ray photoelectron spectroscopy, energy-dispersive X-ray spectroscopy, and high-angular dark field scanning transmission electron microscopy experiments. Our templating approach allows therefore the synthesis of bimetallic nanoballs of tunable porosity and composition.