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Computer experiments play a crucial role when physical experiments are expensive or difficult to be carried out. As a kind of designs for computer experiments, maximin distance designs have been widely studied. Many existing methods for obtaining maximin distance designs are based on stochastic algorithms, and these methods will be infeasible when the run size or number of factors is large. In this paper, we propose some deterministic construction methods for maximin L 2 -distance designs in two to five dimensions based on densest packings. The resulting designs have large L 2 -distances and are mirror-symmetric. Some of them have the same L 2 -distances as the existing optimal maximin distance designs, and some of the others are completely new. Especially, the resulting 2-dimensional designs possess a good projection property. [ABSTRACT FROM AUTHOR]