Constructions and bounds for \((m,t)\)-splitting systems (Q861791)

An \((m,t)\)-splitting system is a collection \(\mathcal B\) of subsets of an \(m\)-element set \(X\) such that for every \(t\)-element subset \(Y\) of \(X\) there exists \(B\in\mathcal B\) with \(| B\cap Y| =\lfloor t/2\rfloor\). The authors give several constructions of \((m,3)\)-splitting systems. Some extensions of these constructions to the general case are discussed.