An infinite class of generalized room squares |
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Authors: | JJ Stiffler IF Blake |
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Institution: | Raytheon Company, Sudbury, Mass. 01776, USA;Department of Electrical Engineering, University of Waterloo, Waterloo, Ont., Canada |
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Abstract: | A generalized Room square of order n and degree k is an array, each cell of which is either empty or contains an unordered k-tuple of a set S, |S| = n, such that each row and each column of the array contains each element of S exactly once and contains each unordered k-tuple of S exactly once. Using a class of Steiner systems and a generalized Room square of order 18 and degree 3 constructed by ad hoc methods, an infinite class of degree 3 squares is constructed. |
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