A positron lifetime experiment is performed on samples produced by the compaction of nanocrystalline Ni3Al powder synthesized by the inert-gas condensation technique. In the lifetime spectrum we observe two components corresponding to defects. Computer (virtual) samples of n-Ni3Al are obtained using molecular dynamics combined with the Metropolis Monte Carlo technique. Positron lifetime calculations are then performed on selected regions of simulated samples. For this purpose, a new computational technique based on a generalization of the atomic superposition method for non-periodic systems was developed. Lifetimes calculated in this way are compared to experiment.