Abstract
Abstract Room squares have been extensively studied and their existence has been completely settled. The balanced Room square problem appears to be much more difficult. The existence problem for these designs is far from complete. In this paper we show how to construct a certain class of balanced Room squares from finite geometries and use recursive constructions for the geometries to produce infinitely many new balanced Room squares. The paper generalizes the concept of a balanced Room square to Kirkman squares with larger block size. Using finite geometries infinitely many balanced Kirkman squares are constructed.
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