Long shortest vectors in low dimensional lattices

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For coprime integers , with , we define the set We study which parameters generate point sets with long shortest distances between the points of the set in dependence of and relate such sets to lattices of a particular form. As a main result, we present an infinite family of such lattices with the property that the normalised norm of the shortest vector of each lattice converges to the square root of the Hermite constant . We obtain a similar result for the generalisation of our construction to 4 and 5 dimensions.

Original languageEnglish
Article number112138
JournalDiscrete Mathematics
Issue number12
Early online date08 Sep 2020
Publication statusEarly online date - 08 Sep 2020


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