The purpose of this paper is to describe the computational algorithmic generation of the high-quality digital halftones (grey/colour patterns). At the beginning, the formal model for generation of the digital halftones, the so-called grey pattern problem (GPP) is introduced. Then, the heuristic algorithm for the solution, in particular, of the grey pattern problem is discussed. Although the algorithm employed does not guarantee the optimality of the solutions found, still superior-quality, near-optimal (and in some cases probably optimal) solutions can be achieved within reasonable computation time. Further, we provide the results of the extensive computational experiments with the newly proposed, extra-large size instance (data set) of the GPP — which is the main contribution of this work. As a confirmation of the quality of the solutions produced, we also give the visual representations of several fine-looking halftone patterns and the reader can judge about the perfection of the images obtained.