  Random sequential addition (RSA) time-dependent packing process, in which
congruent hard hyperspheres are randomly and sequentially placed into a system
without interparticle overlap, is a useful packing model to study disorder in
high dimensions. Of particular interest is the infinite-time {\it saturation}
limit in which the available space for another sphere tends to zero. However,
the associated saturation density has been determined in all previous
investigations by extrapolating the density results for near-saturation
configurations to the saturation limit, which necessarily introduces numerical
uncertainties. We have refined an algorithm devised by us [S. Torquato, O.
Uche, and F.~H. Stillinger, Phys. Rev. E {\bf 74}, 061308 (2006)] to generate
RSA packings of identical hyperspheres. The improved algorithm produce such
packings that are guaranteed to contain no available space using finite
computational time with heretofore unattained precision and across the widest
range of dimensions ($2 \le d \le 8$). We have also calculated the packing and
covering densities, pair correlation function $g_2(r)$ and structure factor
$S(k)$ of the saturated RSA configurations. As the space dimension increases,
we find that pair correlations markedly diminish, consistent with a recently
proposed "decorrelation" principle, and the degree of "hyperuniformity"
(suppression of infinite-wavelength density fluctuations) increases. We have
also calculated the void exclusion probability in order to compute the
so-called quantizer error of the RSA packings, which is related to the second
moment of inertia of the average Voronoi cell. Our algorithm is easily
generalizable to generate saturated RSA packings of nonspherical particles.
