The spectrum of α-resolvable block designs with block size 3

AbstractA balanced incomplete block design D(v, k, λ) is α-resolvable if its blocks can be partitioned into classes such that each point of the design lies in exactly α blocks in each class. Necessary conditions on the parameters of such designs are those required for balanced incomplete block designs (that is, vb = rk, λ(v - 1) = r(k - 1)) together with the conditions k | αv, and α | r. It is shown here that if k = 3 then these conditions are also sufficient for the existence provided that v ≠ 6, α ≠ 1