A first stage of a switching network includes a plurality v of switching matrices each including a predetermined number r of input signal terminals and output signal terminals. At least one different pair of links for signal path connection is provided for outputs of each pair of first stage matrices to some one of b k-input switching matrices of a second stage of the network. Links from any first stage matrix extend to only a portion of the output stage matrices and are arranged in accordance with a balanced, incomplete block design derived from combinatorial theory to distribute the link connections substantially evenly among the second stage matrices. The 2-stage network is itself a block design switching matrix that is useful for building higher order networks. A block design matrix also is combined, through time slot interchanging circuits or another switching stage, with a network of mirror image configuration so that signal path pairs established in the second network are the mirror image of path pairs established for the same communication through the first network.
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