On packing designs with block size 5 and indices 3 and 5

Let V be a finite set of order v. A (V,K,A) packing design of index A and block size IC is a collection of K-element subsets, called blocks, such that every 2-subset of V occurs in at most A blocks. The packing problem is to determine the maximum number of blocks, D(V,K,A), in a packing design. It is well known that D(V,K,A) S [-i [:=~ ~]] : : t(VIK,~), where [xl is the largest integer satisfying x ~ [xl. It is shown here that 0(u,S,3) = ~(u,5,3) for all v = 3 (mod 4) and 0(v,5,s) ~(u,s,5) for all positive integers v ~ 5 with the possible exceptions of v = 28, 32, 34.