  We determine the dimensional dependence of the percolative exponents of the
jamming transition via numerical simulations in four and five spatial
dimensions. These novel results complement literature ones, and establish
jamming as a mixed first-order percolation transition, with critical exponents
$\beta =0$, $\gamma = 2$, $\alpha = 0$ and the finite size scaling exponent
$\nu^* = 2/d$ for values of the spatial dimension $d \geq 2$. We argue that the
upper critical dimension is $d_u=2$ and the connectedness length exponent is
$\nu =1$.
