Some inequalities for multidimensional (0,1)- matrices

Can there exist a (0,1)-matrix of order n and dimension d, such that the sum on any e-dimensional hyperplane of the matrix is a fixed number r? The answer to this question is of importance both for the construction of incomplete block designs and for the investigation of extremal points in the convex sets of multidimensional stochastic matrices. Some necessary conditions that must be fulfilled by the parameters n, d, e, and r are deduced in this paper.