On sublattice determinants in reduced bases

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Pataki, Gabor
Tural, Mustafa
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Abstract
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We prove several inequalities on the determinants of sublattices in LLL-reduced bases. They generalize the inequalities on the length of the shortest vector proven by Lenstra, Lenstra, and Lovasz, and show that LLL-reduction finds not only a short vector, but more generally, sublattices with small determinants. We also prove new upper bounds on the product of the norms of the first few vectors.
Comment: 5 pages
Keywords
Mathematics - Number Theory, Mathematics - Combinatorics, Mathematics - Metric Geometry, Mathematics - Optimization and Control, 11H06, 11H50, 11Y16
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