| Abstract: | Let SSR(v, 3) denote the set of all integer b* such that there exists a RTS(v, 3) with b* distinct triples. In this paper, we determine the set SSR(v, 3) for v ≡ 3 (mod 6) and v ≥ 3 with only five undecided cases. We establish that SSR(v, 3) = P(v, 3) for v ≡ 3 (mod 6), v ≥ 21 and v ≠ 33, 39 where P(v, 3) = {mv, mv + 4, mv + 6, mv + 7, …, 3mv} and mv, = v(v ? 1)/6. As a by‐product, we remove the last two undecided cases for the intersection numbers of Kirkman triple system of order 27, this improves the known result provided in 2 ]. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 275–289, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10037 |
