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We revisit the standard enumeration algorithm for finding the shortest vectors in a lattice, and study how the number of nodes in the associated search tree can be reduced. Two approaches for reducing the number of nodes are suggested. First we show that different permutations of the basis vectors have a big effect on the running time of standard enumeration, and give a class of permutations that give relatively few nodes in the search tree. This leads to an algorithm called hybrid enumerationdoi:10.36244/icj.2019.4.2 fatcat:7jshre4syzb4fjrf5wgjypbgs4