The K- over K+ multiplicity ratio is measured in deep-inelastic scattering, for the first time for kaons carrying a large fraction z of the virtual-photon energy. The data were obtained by the COMPASS collaboration using a 160 GeV muon beam and an isoscalar (LiD)-Li-6 target. The regime of deep-inelastic scattering is ensured by requiring Q(2) > 1 (GeV/c)(2) for the photon virtuality and W > 5 GeV/c(2) for the invariant mass of the produced hadronic system. Kaons are identified in the momentum range from 12 GeV/c to 40 GeV/c, thereby restricting the range in Bjorken-x to 0.01 < x < 0.40. The z-dependence of the multiplicity ratio is studied for z > 0.75. For very large values of z, i.e. z > 0.8, we observe the kaon multiplicity ratio to fall below the lower limits expected from calculations based on leading and nextto-leading order perturbative quantum chromodynamics. Also, the kaon multiplicity ratio shows a strong dependence on the missing mass of the single-kaon production process. This suggests that within the perturbative quantum chromodynamics formalism an additional correction may be required, which takes into account the phase space available for hadronisation. (C) 2018 The Author(s). Published by Elsevier B.V.