Transversal Designs and Doubly-resolvable Designs

A problem which has recently attracted much interest is to arrange the blocks of a (v, k, 1)-BIBD into some of the cells of a square array such that each element of the design occurs in precisely one cell of each row and column of the array. For k = 2, the problem has been completely settled. For k ⩾ 3, two papers have appeared which show that there exist values of v for which this is possible. In this paper, we show that the constructions given in these papers are a special case of a more general result involving transversal designs.