On an estimate related to the homogeneous minimum of the admissible lattice.

In this paper, we have obtained an upper estimate for the norm of the basis vectors of the lattice Λ in terms of the homogeneous minimum of the lattice μ. Such estimates are used to estimate and find the vector and closest vector problems on lattices. In this paper, we essentially use the geometric construction of the basis of an admissible lattice and some properties of matrix arithmetic. [ABSTRACT FROM AUTHOR]