On $\lambda$-packings of pairs by quintuples: $\lambda \equiv 0(mod4)$

Abstract

A $\lambda$-packing of pairs by quintuples of a $v$-set $V$ is a family of $5$-subsets of $V$ (called blocks) such that every $2$-subset of $V$ occurs in at most $\lambda$ blocks. The packing number is defined to be the maximum number of blocks in such a $\lambda$-packing. These numbers are determined here for $\lambda \equiv 0\mathrm{mod}4$ and all integers $v\ge 5$ with the exceptions of $(v,\lambda )\in \{(22,16),(22,36),(27,16)\}$.