  Let $\mathbf x=\{x^{(1)},\dots,x^{(n)}\}$ be a space filling-design of $n$
points defined in $[0{,}1]^d$. In computer experiments, an important property
seeked for $\mathbf x$ is a nice coverage of $[0{,}1]^d$. This property could
be desirable as well as for any projection of $\mathbf x$ onto $[0{,}1]^\iota$
for $\iota<d$ . Thus we expect that $\mathbf
x_I=\{x_I^{(1)},\dots,x_I^{(n)}\}$, which represents the design $\mathbf x$
with coordinates associated to any index set $I\subseteq\{1,\dots,d\}$, remains
regular in $[0{,}1]^\iota$ where $\iota$ is the cardinality of $I$. This paper
examines the conservation of nice coverage by projection using spatial point
processes, and more specifically using the class of determinantal point
processes. We provide necessary conditions on the kernel defining these
processes, ensuring that the projected point process $\mathbf{X}_I$ is
repulsive, in the sense that its pair correlation function is uniformly bounded
by 1, for all $I\subseteq\{1,\dots,d\}$. We present a few examples, compare
them using a new normalized version of Ripley's function. Finally, we
illustrate the interest of this research for Monte-Carlo integration.
