  Let $ r, s>0 $. For a given probability measure $P$ on $\mathbb{R}^d$, let
$(\alpha_n)_{n \geq 1}$ be a sequence of (asymptotically) $L^r(P)$- optimal
quantizers. For all $\mu \in \mathbb{R}^d $ and for every $\theta >0$, one
defines the sequence $(\alpha_n^{\theta, \mu})_{n \geq 1}$ by : $\forall n \geq
1, \alpha_n^{\theta, \mu} = \mu + \theta(\alpha_n - \mu) = \{\mu + \theta(a-
\mu), a \in \alpha_n \} $. In this paper, we are interested in the asymptotics
of the $L^s$-quantization error induced by the sequence $(\alpha_n^{\theta,
\mu})_{n \geq 1}$. We show that for a wide family of distributions, the
sequence $(\alpha_n^{\theta, \mu})_{n \geq 1}$ is $L^s$-rate-optimal. For the
Gaussian and the exponential distributions, one shows how to choose the
parameter $\theta$ such that $(\alpha_n^{\theta, \mu})_{n \geq 1}$ satisfies
the empirical measure theorem and probably be asymptotically $L^s$-optimal.
