Pairwise balanced designs with block sizes 4 and 8

Let K be a set of positive integers. A pairwise balanced design (PBD) of index unity B(K,l;v) is a pair (X/~) where X is a v-set (of points) and B is a collection of subsets of X (called blocks) with sizes from K such that every pair of distinct points of X is contained in exactly one block of~. A necessary condition for the existence of a PBD B({4,8},I;v) is v-0 or l(mod 4). It is shown that this necessary condition is also sufficient for all v ~ 4 with 11 exceptions and 25 possible exceptions of which 177 is the largest. We briefly mention some applications to other types of combinatorial structures.