A new class of symmetric \((v,k,\lambda)\)-designs (Q1335418)

\textit{E. Spence}, \textit{V. Tonchev} and \textit{Tran van Trung} [J. Comb. Designs 1, 65-68 (1993)] constructed a symmetric (160,54,18)-design and \textit{E. Spence} [Eur. J. Comb. 14, No. 2, 131-136 (1993; Zbl 0777.05018)] generalized their construction method to get an infinite family of symmetric designs. In the present paper, the authors show that the Spence construction can be generalized even further by using \(\omega\)-circulant matrices. The derived family is given by \(v= p^ s(q^{2m}- 1)/(q- 1)\), \(k= q^{2m-1} p^{s-1}\), \(\lambda= p^{s-1} q^{2m-2}(p^{s-1}- 1)/(p- 1)\), where \(p\) is a prime and \(q\) is a prime power with \(q= (p^ s- 1)/(p- 1)\).