Intersection Numbers of Kirkman Triple Systems

LetJR(v) denote the set of all integersksuch that there exists a pair ofKTS(v) with preciselyktriples in common. In this article we determine the setJR(v) forv≡3 (mod 6) (only 10 cases are left undecided forv=15, 21, 27, 33, 39) and establish thatJR(v)=I(v) forv≡3 (mod 6) andv⩾45, whereI(v)={0, 1, …, tv−6, tv−4, tv} andtv=16v(v−1).