Three Constructions of Covers

Abstract

Three general constructions for covers are given. A cover is a set of $k$-subsets of a $v$-set, $V$, such that every $t$-subset of $V$ is contained in at least one of the $k$-sets. These constructions use the idea of dividing the $v$-set into either two or three equal sized subsets. The last two constructions also use the idea of establishing a correspondence between the two equal subsets in order to facilitate the construction.