The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we obtain time-optimal and deterministic solutions for the fundamental communication task of multi-broadcast. The proposed solutions are completely uniform, i.e., independent of the network and problem parameters. The originality of our approach lies in the use of (combinatorial) group testing strategies, originally developed in the centralized context. We improve on previous solutions to multi-broadcast by giving efficiently constructible solutions, that is, with local computation cost polynomial in the identifiers' range.