  The Korkine-Zolotareff (KZ) reduction is a widely used lattice reduction
strategy in communications and cryptography. The Hermite constant, which is a
vital constant of lattice, has many applications, such as bounding the length
of the shortest nonzero lattice vector and orthogonality defect of lattices.
The KZ constant can be used in quantifying some useful properties of KZ reduced
matrices. In this paper, we first develop a linear upper bound on the Hermite
constant and then use the bound to develop an upper bound on the KZ constant.
These upper bounds are sharper than those obtained recently by the first two
authors. Some examples on the applications of the improved upper bounds are
also presented.
