On resolvable designs

AbstractA balanced incomplete block design (BIBD) B[k, λ;v] is an arrangement of v elements in blocks of k elements each, such that every pair of elements is contained in exactly λ blocks. A BIBD B[k, 1;v] is called resolvable if the blocks can be partitioned into (v−1)(k−1) families each consisting of v/k mutually disjoint blocks. Ray-Chaudhuri and Wilson [8] proved the existence of resolvable BIBD's B[3, 1; v] for every v≡3 (mod 6). In addition to this result, the existence is proved here of resolvable BIBD's B[4, 1; v] for every v≡4 (mod 12)