LIPIcs - Leibniz International Proceedings in Informatics. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
We show that for any n-dimensional lattice ? ? ??, the torus ??/? can be embedded into Hilbert space with O(?{nlog n}) distortion. This improves the previously best known upper bound of O(n?{log n}) shown by Haviv and Regev (APPROX 2010, J. Topol. Anal. 2013) and approaches the lower bound of ?(?n) due to Khot and Naor (FOCS 2005, Math. Ann. 2006)
