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This article present a concise estimate of upper and lower bound on thecardinality containing shortest vector in a lattice reduced by blockKorkin-Zolotarev method (BKZ) for different value of the block size. Paper showhow density affect to this cardinality, in form of the ratio of shortest vectorsize and sucessive minimal. Moreover we give upper estimate of cardinality forcritical and Goldstein-Mayer lattices.

Upper and lower bound on the cardinality containing shortest vectors in a lattice reduced by block Korkin-Zolotarev method (Russian)