Near-factorizations of dihedral groups

We investigate near-factorizations of nonabelian groups, concentrating on dihedral groups. We show that some known constructions of near-factorizations in dihedral groups yield equivalent near-factorizations. In fact, there are very few known examples of nonequivalent near-factorizations in dihedral or other nonabelian groups; we provide some new examples with the aid of the computer. We also analyse a construction for near-factorizations in dihedral groups from near-factorizations in cyclic groups, due to P\^{e}cher, and we investigate when nonequivalent near-factorizations can be obtained by this method.