Transversal Designs and Doubly-resolvable Designs
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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.
[1] Richard M. Wilson,et al. On resolvable designs , 1972, Discret. Math..
[2] Scott A. Vanstone,et al. On the existence of doubly resolvable Kirkman systems and equidistant permutation arrays , 1980, Discret. Math..
[3] W. D. Wallis,et al. The existence of Room squares , 1975 .