On the maximum number of disjoint Steiner triple systems

Let D(v) be the maximum number of pairwise disjoint Steiner triple systems of order v. We prove that D(3v)>=2v+D(v) for every v = 1 or 3 (mod 6), v>=3. As a corollary, we have D(3^n)=3^n-2 for every n>=1.