On some infinite series of (r,1)-designs Original Research Article

(r,1)-designs are linear spaces with v points where every point lies on exactly r lines. In this paper some infinite series of (r,1)-designs are discussed establishing the following existence result. Let Δ=v−r be the class of the (r,1)-design. For Δ⩽4 the necessary and sufficient conditions are determined such that there is an (r,1)-design with a certain point-type distribution. For larger values of Δ some further series are discussed.