Packing designs with block size 6 and index 5

A (v, k{cyrillic}, λ) packing design of order v, block size k{cyrillic} and index λ is a collection of k{cyrillic}-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. The only previous work on the packing problem with k{cyrillic}=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{cyrillic}=6 and λ=5 and all positive integers v with the possible exceptions of v=41, 47, 53, 59, 62, 71.