  Using the Parametric Geometry of Numbers introduced recently by W.M. Schmidt
and L. Summerer and results by D. Roy, we show that German's transference
inequalities between the two most classical exponents of uniform Diophantine
approximation are optimal. Further, we establish that the spectrum of the $n$
uniform exponents of Diophantine approximation in dimension $n$ is a subset of
$\mathbb{R}^n$ with non empty interior. Thus, no Jarn\'ik-type relation holds
between them.
