We analyze the capacity of future $Z$-factories to search for heavy neutrinos with their mass from 10 to 85 GeV. The heavy neutrinos $N$ are considered to be produced via the process $e^+e^-to Zto u N$ and to decay into an electron or muon and two jets. By means of Monte Carlo simulation of such signal events and the Standard Model background events, we obtain the upper bounds on the cross sections $sigma(e^+e^-to u Nto uell jj)$ given by the $Z$-factories with integrated luminosities of 0.1, 1 and 10 ab$^{-1}$ if no signal events are observed. Under the assumption of a minimal extension of the Standard Model in the neutrino sector, we also present the corresponding constraints on the mixing parameters of the heavy neutrinos with the Standard Model leptons, and find they are improved by at least one order compared to current experimental constraints.
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