Correction to: “Exponential bounds on the number of designs with affine parameters”

Abstract

It is well known that the number of designs with the parameters of a classical design having as blocks the hyperplanes in PG(n, q) or AG(n, q), n ≥ 3, grows exponentially. This result was extended recently [5] to designs having the same parameters as a projective geometry design whose blocks are the d-subspaces of PG(n, q), for any 2 ≤ d ≤ n−1. In this paper, exponential lower bounds are proved on the number of non-isomorphic designs having the same parameters as an affine geometry design whose blocks are the d-subspaces of AG(n, q), for any 2 ≤ d ≤ n−1. Exponential bounds are also proved for the number of resolvable designs with these parameters. q 2011 Wiley Periodicals, Inc. J Combin Designs 19: