Packing designs with block size 6 and index 5

Assaf, A.M., A. Hartman and N. Shalaby, Packing designs with block size 6 and index 5, Discrete Mathematics 103 (1992) 121-128. A (v, K, A) packing design of order v, block size K and index 1 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 I blocks. The packing problem is to determine the maximum number of blocks in a packing design. The only previous work on the packing problem with K = 6 concerns itself with the cases where the maximum packing design is in fact a balanced incomplete block design. In this paper we solve the packing problem with K = 6 and A = 5 and all positive integers v with the possible exceptions of v = 41, 47, 53, 59, 62, 71.