@Book{1987109260, author="Roberts, Ian T. and D'Arcy, Sue and Egan, Judith and Gr{\"u}ttm{\"u}ller, Martin", title="An improved bound on the cardinality of the minimal pairwise balanced designs on 18 points with maximum block size 4", series="Preprints aus dem Institut f{\"u}r Mathematik", year="2005", address="Germany; Rostock", abstract="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. ", note="Ian T. Roberts, Sue D'Arcy, Judith Egan, Martin Gr{\"u}ttm{\"u}ller", doi="10.18453/rosdok_id00005893", url="https://purl.uni-rostock.de/rosdok/id00005893", url="https://doi.org/10.18453/rosdok_id00005893", language="English" }