Ian T. Roberts, Sue D'Arcy, Judith Egan, Martin Grüttmüller
An Improved Bound on the Cardinality of the Minimal Pairwise Balanced Designs on 18 Points with Maximum Block Size 4
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

05B30 Other designs, configurations, See also {51E30}

51E30 Other finite incidence structures, See also {05B30}

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 $31\leq g^{(4)}(18)\leq 33$.
In this paper we show that $g^{(4)}(18) \neq 31$.

Keywords: pairwise balanced design