The intersection numbers of KTSs with a common parallel class

In this paper, the intersection numbers of KTSs with a common parallel class are investigated. Denote by J1[u]J1[u] the set of all integers kk such that there is a pair of KTS(3u3u)s with a common parallel class intersecting in k+uk+u triples, uu of them being the triples of the common parallel class. It has been established that J1[u]={0,1,…,3(u2)−6,3(u2)−4,3(u2)} for any odd integer u≥7u≥7 and u≠9,11,13,17,19u≠9,11,13,17,19. For u=9,11,13,17,19u=9,11,13,17,19, there are 11 cases that are left undecided.