A Technique for Constructing Symmetric Designs

Let M be a set of incidence matrices of symmetric (v,k,)-designs and G a group of mappings M M. We give a sufficient condition for the matrix W M, where M M and W is a balanced generalized weighing matrix over G, to be the incidence matrix of a larger symmetric design. This condition is then applied to the designs corresponding to McFarland and Spence difference sets, and it results in four families of symmetric (v,k, )-designs with the following parameters k and (m and d are positive integers, p and q are prime powers): (i) ; (ii) ; (iii) ; (iv) .