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Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
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Residual design (BIBD) with repeated blocks
Simple BIBD are defined as those designs in which incindence relation is "is element". So effectively blocks are subsets of points. Equivalently there should be no "repeating blocks" ie. blocks that a …