  In this paper, we present a comprehensive study of $\Upsilon$ inclusive
production in $Z$ boson decay, including the first complete
next-to-leading-order calculations of the color-octet (CO) contributions. With
the inclusion of the newly-calculated remarkable QCD corrections, the CO
processes exhibit crucially phenomenological significance in the existing
predictions built on the color-singlet mechanism. We also include the
exhaustive evaluations of the feed-down contributions, which remained ignored
in the literature, and find them to be considerable. Summing up all the
contributions, the $\mathcal{B}_{Z \to \Upsilon(nS)+X}$ still notably
undershoot the data released by the L3 Collaboration.
