Martin Grüttmüller, Rolf Rees
Necessary Existence Criteria for Mandatory Representation Designs MRD(4,k;v)
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
MSC:
Abstract: A mandatory representation design MRD $(K;v)$ is a pairwise balanced
design on
$v$ points with block sizes from the set $K$ in which for each $k\in K$
there is at least one block in the design of size $k$.
A survey of known results on MRDs has been given in [R2] by Rees.
MRDs with $K=\{3,k\}$ have been extensively studied
by Mendelsohn and Rees [MR], Rees [R], Rees and Gr\"uttm\"uller [GR2]
and Gr\"uttm\"uller [G, G2].
In this paper, we investigate necessary conditions for the existence
of MRDs with $K=\{4,k\}$.
Keywords: Mandatory Representation Design, Pairwise Balanced Design, necessary existence criteria