We study the problem that among all hypergraphs with e edges of ranks l(1), ..., l(e) an v vertices, which hypergraph has the least number of vertex-covers of size e. The problem is very difficult and we only get some partial answers. We show an application of our results to improve the error-tolerance of a pooling design proposed in the literature. (c) 2008 Elsevier B.V. All rights reserved.
