Pooling semilattices and non-adaptive pooling designs

In Huang and Weng (2004), Huang and Weng introduced pooling spaces, and constructed pooling designs from a pooling space. In this paper, we introduce the concept of pooling semilattices and prove that a pooling semilattice is a pooling space, then show how to construct pooling designs from a pooling semilattice. Moreover, we give many examples of pooling semilattices and thus obtain the corresponding pooling designs.