Abstract
The intersection of two Steiner triple systems ( X, A) and ( X, B) is the set A boolean AND B. The. ne intersection problem for Steiner triple systems is to determine for each nu, the set I (nu), consisting of all possible pairs (m, n) such that there exist two Steiner triple systems of order nu whose intersection I satisfies vertical bar boolean OR(A is an element of I) A vertical bar = m and vertical bar I vertical bar = n. We show that for nu = 1 or 3 (mod 6), vertical bar I (nu)vertical bar = Theta(nu(3)), where previous results only imply that vertical bar I (nu)vertical bar = Omega(nu(2)).