On packing designs with block size 5 and index 4

A (v,k,λ) packing design of order v, block size k, and index λ is a collection of k-element subsets, called blocks, of a v-set, V, such that every 2-subset of V occurs in at most λ blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper we solve the packing problem with k=5, λ=4, and all positive integers v. © 1989.