  Depending on the Higgs-boson and top-quark masses, $M_H$ and $M_t$, the
effective potential of the Standard Model at finite (and zero) temperature can
have a deep and unphysical stable minimum $\langle \phi(T)\rangle$ at values of
the field much larger than $G_F^{-1/2}$. We have computed absolute lower bounds
on $M_H$, as a function of $M_t$, imposing the condition of no decay by thermal
fluctuations, or quantum tunnelling, to the stable minimum. Our effective
potential at zero temperature includes all next-to-leading logarithmic
corrections (making it extremely scale-independent), and we have used pole
masses for the Higgs-boson and top-quark. Thermal corrections to the effective
potential include plasma effects by one-loop ring resummation of Debye masses.
All calculations, including the effective potential and the bubble nucleation
rate, are performed numerically, and so the results do not rely on any kind of
analytical approximation. Easy-to-use fits are provided for the benefit of the
reader. Conclusions on the possible Higgs detection at LEP-200 are drawn.
