We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let N>0 and L\in Z_\ge 2 . A multiple packing is a set C of points in Rn such that any point in Rn lies in the intersection of at most L-1 balls of radius \sqrt nN around points in C . Given a well-known connection with coding theory, multiple packings can be viewed as the Euclidean analog of list-decodable codes, which are well-studied for finite fields. In this paper, we derive the best known lower bounds on the optimal density of list-decodable infinite constellations for constant L under a stronger notion called average-radius multiple packing. To this end, we apply tools from high-dimensional geometry and large deviation theory. © 1963-2012 IEEE.