This paper presents results on charged Higgs boson production, based on LEP data collected at $\sqrt{s} = 172$ GeV, that complement the previous DELPHI results obtained at centre of mass energies up to 161 GeV. %The analysis is based on LEP data collected at $\sqrt{s} = 172$ GeV. The charged Higgs bosons are assumed to be pair produced and to decay either into a quark pair %, identified as cs, or into $\tau\nu_{\tau}$. The three different possible final states are included in the analysis. Data from ring imaging Cherenkov and microvertex detectors are used to identify the quarks as a cs pair. %No significant signal was found. The number of candidates found is compatible with the background expected from standard processes. Combining the results of the present analysis with those of the previous analysis at lower energies, a new lower mass limit for the charged Higgs boson is set at 54.5 GeV/$c^2$.

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