Multiple packing is a natural generalization of sphere packing . We revisit the problem of high-dimensional multiple packing in Euclideanspace . We study the multiplepacking problem for both bounded point sets and unbounded point sets . We derive various bounds on the largest possible density of a multiple packing . A related notion called average-radiusmultiple packing is also studied . Some of our lower bounds pin down theasymptotics of certain ensembles of average- radius list-decodable codes, e.g.,(expurgated) Gaussian codes and Poisson Point Processes . To thisend, we apply tools from geometry and large deviation theory to thisend of the problem . We use tools from high-dimension geometry and other large deviation theories to find out what the error exponent is of independent interest beyond multiple packings are of interest beyond the multiple packing theory . For more information, please visit

Author(s) : Yihan Zhang, Shashank Vatedka

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Keywords : packing - multiple - bounds - problem - point -

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