The Intersection Numbers of Nearly Kirkman Triple Systems

In this paper, we investigate the intersection numbers of nearly Kirkman triple systems. J(N)[v] is the set of all integers k such that there is a pair of NKTS(v)s with a common uncovered collection of 2-subset intersecting in k triples. It has been established that J(N) left perpendicular v right perpendicular = {0, 1,...,v(v-2)/6 - 6, v(v-2)/6 - 4, v(v-2)/6} for any integers v 0 (mod 6) and v >= 66. For v <= 60, there are 8 cases left undecided.