A note on square divisible designs

We consider square divisible designs with parameters n, m, k=r, 0 and . We show that being disjoint induces an equivalence relation on the block set of such a design and that any two disjoint blocks meet precisely the same point classes. Also, the intersection number of two blocks depends only on their equivalence classes. The number of blocks disjoint with a given block is at most n–1; equality holds for all blocks iff the dual of the given design is also divisible with the same parameters. We then give a few applications.The author gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft via a Heisenberg grant during the time of this research.