  Future energy-frontier electron-positron colliders will be capable of
high-precision studies of top quark properties. The measurement of the top-pair
production cross section around the threshold provides access to the mass of
the top quark in theoretically well-defined schemes, with statistical
uncertainties of 20 MeV or less, depending on the assumed integrated luminosity
of the measurement. At this level of precision, experimental and theory
systematics are likely to become important or even dominant. This contribution
presents a first analysis of the impact of the remaining uncertainties of the
recently completed calculation of the top pair production cross section at
NNNLO QCD including the exchange of Higgs bosons on the extraction of the top
quark mass from a threshold scan. The analysis is based on reconstruction
efficiencies and background levels obtained in full simulation studies for
CLIC, combined with signal cross sections from the higher-order calculations.
To assess possible differences between different collider options, the study is
performed in the context of CLIC, ILC and FCC-ee by considering the differences
in the luminosity spectra.
