An infinite family of symmetric designs

In this paper, using the construction method of [3], we show that if q>2 is a prime power such that there exists an affine plane of order q-1, then there exists a strongly divisible 2-(q-1)(q^h-1), q^h-1(q-1), q^h-1) design for every h>=2. We show that these quasi-residual designs are embeddable, and hence establish the existence of an infinite family of symmetric 2-(q^h^+^1-q+1,q^h, q^h^-^1) designs. This construction may be regarded as a generalisation of the construction of [1, Chapter 4, Section 1] and [4].