Abstract. The best previous lower bounds for kissing numbers in dimensions 25-31 were constructed using a set S with |S| = 480 of minimal vectors of the Leech Lattice, Λ 24 , such that x, y ≤ 1 for any distinct x, y ∈ S. Then, a probabilistic argument based on applying automorphisms of Λ 24 gives more disjoint sets S i of minimal vectors of Λ 24 with the same property. Cohn, Jiao, Kumar, and Torquato proved that these subsets give kissing configurations in dimensions 25-31 of given size linear in the sizes of the subsets. We achieve |S| = 488 by applying simulated annealing. We also improve the aforementioned probabilistic argument in the general case. Finally, we greedily construct even larger S i 's given our S of size 488, giving increased lower bounds on kissing numbers in R 25 through R 31 .
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