On a Huge Family of Non-Schurian Schur Rings

In his famous monograph on permutation groups, H. Wielandt gives an example of a Schur ring over an elementary abelian group of order p(2) (p > 3 is a prime), which is non-schurian, that is, it is the transitivity module of no permutation group. Generalizing this example, we construct a huge family of non-schurian Schur rings over elementary abelian groups of even rank.