Three Constructions of Covers

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.