Balanced generalized handcuffed designs (Q1208361)

A balanced handcuffed design consists of a \(v\)-set \(V\) and a set of \(b\) ordered \(k\)-subsets \((a_{i,1},\dots,a_{i,k})\) of \(V\), for \(i=1\) to \(b\), such that for \(s=1,2,\dots,t\) the sets \(\{a_{i,j},a_{i,j+1},\dots,a_{i,j+s-1}\}\) where \(1\leq j\leq k-s+1\) cover the \(s\)-subsets of \(V\) a constant \(\lambda_ s\) times. This concept specializes the generalized handcuffed designs of the author and generalizes the handcuffed designs of Hung and Mendelsohn. The author describes a method of differences for the construction of such designs. In particular he gives a complete solution for \(k=3\), \(t=3\) and \(\lambda_ 3=1\), together with several other examples.