Bounding the Higgs Boson Mass in the Next-to-Minimal Supersymmetric Standard Model

We discuss the upper bound on the lightest CP-even Higgs boson mass in the next-to-minimal supersymmetric standard model within the framework of a low energy renormalisation group analysis. We find $m_h$ < 146 GeV for $m_t$ = 90 GeV, decreasing to $m_h$ < 123 GeV for $m_t$ = 180 GeV.