The set of values of b for which there exist block designs with b blocks

Let B denote the set of values of b for which there exists a block design with b blocks and for image, let image denote the subset of B determined by the designs with block size k. We present some information about B and the sets image. In particular, we discuss, for certain integers h, the question as to whether there exist integers k and image such that the equation image has infinitely many solutions image satisfying image and image. The study is restricted to the case image.