Abstract
It is well-known that every lattice L has a basis consisting of relatively short vectors. To state a quantitative version of this fact, let 21(L) denote the i-th successive minimum of L, which is the smallest value such that there are i linearly independent vectors in L in the ball {x: [I x II _-< ~.i(L)}. In particular, let A, be the minimal constant such that every lattice of rank n possesses a basis which satisfies
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