A new class of symmetric (v, k, λ)-designs

Abstract

We construct new families of symmetric (v, k, λ)-designs with parameters

$$\begin{gathered} v = p^s \cdot (q^{2m} - 1)/(q - 1). \hfill \\ k = q^{2m - 1} \cdot p^{s - 1} , \hfill \\ \lambda = p^{s - 1} \cdot q^{2m - 2} \cdot (p^{s - 1} - 1)(p - 1) \hfill \\ \end{gathered} $$

wherep is a prime andq is a prime power with

$$q = (p^{s - 1} - 1)/(p - 1).$$

The orders of our designs aren=p ^2s−2·q ^2m−2.