An improved bound on the cardinality of the minimal pairwise balanced designs on 18 points with maximum block size 4

10.18453/rosdok_id00005893 Roberts, Ian T. Ian T. Roberts D’Arcy, Sue Sue D’Arcy Egan, Judith Judith Egan Grüttmüller, Martin Martin Grüttmüller http://d-nb.info/gnd/122522559 An improved bound on the cardinality of the minimal pairwise balanced designs on 18 points with maximum block size 4 University of Rostock, Institute of Mathematics 2005 510 Mathematics 2005 en https://purl.uni-rostock.de/rosdok/id00005893 urn:nbn:de:gbv:28-rosdok_id00005893-0 The cardinality of the minimal pairwise balanced designs on v elements with largest block size k is denoted by g(k)(v). It is known that 31 <= g(4)(18) <= 33. In this paper we show that g(4)(18) =/ 31.