  Recently, Church-Miller-Nagpal-Reinhold [arXiv:1706.03845] obtained linear
stable ranges for the integral cohomology of ordered configuration spaces, in
the sense of representation stability. We note that the constants in these
linear stable ranges can be further improved for an orientable manifold of
dimension at least 3. The idea is to simply exploit the sparsity of Totaro's
spectral sequence.
