Packing designs with block size 5 and indexes 8, 12, 16 (Q1185878)

A \((v,k,\lambda)\) packing design of order \(v\), block size \(k\), and index \(\lambda\) is a collection of \(k\)-element subsets, called blocks, of a set \(V\) such that every 2-subset of \(V\) occurs in at most \(\lambda\) blocks. The packing problem is to determine the maximum number of blocks in a packing design. In this paper the packing problem with \(k=5\), \(\lambda=8,\) 12, 16, and all positive integer \(v\) with the possible exceptions of \((v,\lambda)=(19,16)\) (22,16) (24,16) (27,16) (28,12) has been solved.