For positive integers n≥k≥t, a collection MJX-tex-caligraphicscriptB 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 MJX-tex-caligraphicscriptB. In this paper, we investigate the existence of the maximum 3‐packings whenever n is sufficiently larger than k. When n≢20.3em(mod0.3emk−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.