On resolvable designs

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