On small packing and covering designs with block size 4

A packing (respectively covering) 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 (at least) λ blocks. The packing (covering) problem is to determine the maximum (minimum) number of blocks in a packing (covering) design. Motivated by the recent work of Assaf [1] [2], we solve the outstanding packing and covering problems with block size 4.