Packing cliques in 3-uniform hypergraphs

For positive integers n >= k >= t, a collection B of k-subsets of an n-set X is called a t-packing if every t-subset of X appears in at most one set in B. In this paper, we investigate the existence of the maximum 3-packings whenever n is sufficiently larger than k. When n not equivalent to 2(modk-2), the optimal value for the size of a 3-packing is settled. In other cases, lower and upper bounds are obtained where mostly differ by an additive constant depending only on k but one case that they differ by a linear bound in n.