For
m
,
d
∈
N
m, d \in {\mathbb N}
, a jittered (or stratified) sampling point set
P
P
having
N
=
m
d
N = m^d
points in
[
0
,
1
)
d
[0,1)^d
is constructed by partitioning the unit cube
[
0
,
1
)
d
[0,1)^d
into
m
d
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
>
0
c > 0
and
C
C
such that for all
d
d
and all
m
≥
d
m \ge d
the expected non-normalized star discrepancy of a jittered sampling point set satisfies
\[
c
d
m
d
−
1
2
1
+
log
(
m
d
)
≤
E
D
∗
(
P
)
≤
C
d
m
d
−
1
2
1
+
log
(
m
d
)
.
c \,dm^{\frac {d-1}{2}} \sqrt {1 + \log (\tfrac md)} \le {\mathbb E} D^*(P) \le C\, dm^{\frac {d-1}{2}} \sqrt {1 + \log (\tfrac md)}.
\]
This discrepancy is thus smaller by a factor of
Θ
(
(
1
+
log
(
m
/
d
)
m
/
d
)
1
/
2
)
\Theta \big (\big (\frac {1+\log (m/d)}{m/d}\big )^{1/2}\big )
than the one of a uniformly distributed random point set (Monte Carlo point set) of cardinality
m
d
m^d
. This result improves both the upper and the lower bound for the discrepancy of jittered sampling given by Pausinger and Steinerberger [J. Complexity 33 (2016), pp. 199–216]. It also removes the asymptotic requirement that
m
m
is sufficiently large compared to
d
d
.