Before revision: In this paper we take advantage of a recently published algorithm for computing the number of realizations of minimally rigid graphs . Combining computational results with the theory of constructing new rigid graphs by gluing, we give a new lower bound on the maximal possible number of  realizations for graphs with a given number of vertices.
After revision: In this paper we take advantage of a recently published algorithm , which is the fastest available method, although its complexity is still exponential . Combining computational results with the theory of constructing new rigid graphs by gluing, we give a new lower bound on the maximal possible number of realizations for graphs with a given number of vertices.