Whate+e−collider could make a "no-lose" search for minimal supersymmetric standard model Higgs bosons?

The lightest $\mathrm{CP}$-even Higgs boson $h$ in the minimal supersymmetric standard model (MSSM) has a mass upper bound depending on the top quark and squark masses. An $e^{+}{e}^{-}$ collider with enough energy and luminosity to produce $h+Z$ at measurable rates up to the maximum $h$ mass would cover the entire MSSM parameter space if $h+A$ production was also searched for. We explore the energy and/or luminosity needed for various top quark and squark masses. For $m_t=150\mathrm{}$ GeV and a 1 TeV supersymmetric mass scale, a 230 GeV collider with 10 ${\mathrm{fb}}^{-1\mathrm{}}$ luminosity would suffice, based on $e^{+}{e}^{-}\to \mathrm{hZ}$, $\mathrm{hA}\to \tau \tau \mathrm{jj}$ signals. With future $b$ tagging, other channels will contribute important additional signals and the luminosity requirements will be lowered by up to an order of magnitude.