Martin Gruettmueller
On the Existence of Mandatory Representation Designs with Block Sizes 3 and k
Preprint series: Preprints aus dem Fachbereich Mathematik, Universitt Rostock

MSC:

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

Abstract: A mandatory representation design $\MRD[v,K]$ is a pairwise balanced design
on $v$ points with block sizes from $K$ in which for each $k \in K$ there is a
block in the design of size $k$.
Mendelsohn and Rees \cite{menr88} investigated the existence of \MRD$[v,K]$'s,
where $3 \in K$.
In this report we consider additional necessary conditions,
where $K = \{3,k\}$.
These conditions are proved to be sufficient for $4 \leq k \leq 50$ with
one genuine exception.
Keywords: combinatorial designs, mandatory representation designs, pairwise balanced designs