  Random sequential adsorption of straight rigid rods of length $k$ ($k$-mers)
on a simple cubic lattice has been studied by numerical simulations and
finite-size scaling analysis. The calculations were performed by using a new
theoretical scheme, whose accuracy was verified by comparison with rigorous
analytical data. The results, obtained for \textit{k} ranging from 2 to 64,
revealed that (i) in the case of dimers ($k=2$), the jamming coverage is
$\theta_j=0.918388(16)$. Our estimate of $\theta_j$ differs significantly from
the previously reported value of $\theta_j=0.799(2)$ [Y. Y. Tarasevich and V.
A. Cherkasova, Eur. Phys. J. B \textbf{60}, 97 (2007)]; (ii) $\theta_j$
exhibits a decreasing function when it is plotted in terms of the $k$-mer size,
being $\theta_j (\infty)= 0.4045(19)$ the value of the limit coverage for large
$k$'s; and (iii) the ratio between percolation threshold and jamming coverage
shows a non-universal behavior, monotonically decreasing with increasing $k$.
