Malcolm Greig, Martin Grüttmüller, Sven Hartmann
Pairwise Balanced Designs whose Block Size Set Contains Seven and Thirteen
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
05B30 Other designs, configurations, See also {51E30}
51E30 Other finite incidence structures, See also {05B30}
Abstract: In this paper, we investigate the PBD-closure of sets $K$
with $\{7,13\}\subseteq K \subseteq \{7,13,19,25,31,37,43\}$.
In particular, we show that \kong v16, $v\geq \upperbound$
implies $v\in B(\{7,13\})$.
As a preliminary result, many new $13$-GDDs of type $13^q$
and resolvable BIBD with block size $6$ or $12$ are also constructed.
Furthermore, we show some elements to be not essential in a
Wilson bases for the PBD-closed set $\{v:\kong v16, v\geq 7 \}$.

Keywords: pairwise balanced design, PBD closure, Wilson basis