  We show that on an $n=24m+8k$-dimensional even unimodular lattice, if the
shortest vector length is $\geq 2m$, then as the number of vectors of length
$2m$ decreases, the secrecy gain increases. We will also prove a similar result
on general unimodular lattices. Furthermore, assuming the conjecture by
Belfiore and Sol\'e, we will calculate the difference between inverses of
secrecy gains as the number of vectors varies. Finally, we will show by an
example that there exist two lattices in the same dimension with the same
shortest vector length and the same kissing number, but different secrecy
gains.
