  For $m, d \in {\mathbb N}$, a jittered sampling point set $P$ having $N =
m^d$ points in $[0,1)^d$ is constructed by partitioning the unit cube $[0,1)^d$
into $m^d$ axis-aligned cubes of equal size and then placing one point
independently and uniformly at random in each cube. We show that there are
constants $c \ge 0$ and $C$ such that for all $d$ and all $m \ge d$ the
expected non-normalized star discrepancy of a jittered sampling point set
satisfies \[c \,dm^{\frac{d-1}{2}} \sqrt{1 + \log(\tfrac md)} \le {\mathbb E}
D^*(P) \le C\, dm^{\frac{d-1}{2}} \sqrt{1 + \log(\tfrac md)}.\]
  This discrepancy is thus smaller by a factor of
$\Theta\big(\sqrt{\frac{1+\log(m/d)}{m/d}}\,\big)$ than the one of a uniformly
distributed random point set of $m^d$ points. This result improves both the
upper and the lower bound for the discrepancy of jittered sampling given by
Pausinger and Steinerberger (Journal of Complexity (2016)). It also removes the
asymptotic requirement that $m$ is sufficiently large compared to $d$.
