An infinite class of generalized room squares

A generalized Room square G of order n and degree k is an ^n^-^1^k^-^1 x ^n^-^1^k^-^1 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 G 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.