Packings with Block Size Five and Index One: $v\equiv 2(\mathrm{mod}4)$

Abstract

We use the results on $5$-GDDs to obtain optimal packings with block size five and index one. In particular, we prove that if $v\equiv 2,6,10(\mathrm{mod}20)$, there exists an optimal packing with block size five on $v$ points with at most $32$ possible exceptions. Furthermore, if $v\equiv 14,18(\mathrm{mod}20)$, there exists an optimal packing with block size five on $v$ points with a finite (large) number of possible exceptions.