Balanced generalized handcuffed designs
Abstract The definition of balanced generalized handcuffed designs (BHD) is of course more specific than that of the generalized handcuffed designs that we introduced in 1987. In the first part of this paper, we present a particular property of a BHD, which is not necessarily that of a generalized handcuffed design. Then, we provide the reader with a general procedure that enables one to obtain such designs, and is called a ‘difference method’. We also show how this difference method can be made more useful in the case where the set V on which a BHD is constructed is the residue classes of integers mod V . The third part of this paper deals with the problem of the existence of a BHD; and a solution is given for a particular case. We assume that the method applied for solving this problem will allow for the constructing of many more theorems analogous to Theorem 3.