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

AbstractA (υ, κ, λ) packing design of order υ, block size κ, and index λ is a collection of κ-element subsets, called blocks of a 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 κ = 5, λ = 8, 12, 16, and all positive integers υ with the possible exceptions of (υ, λ) = (19, 16) (22, 16) (24, 16) (27, 16) (28, 12)