We consider the production of strange particles in relativistic nucleus-nucleus collisions. We employ a quark-gluon plasma (QGP) formalism, incorporating the production of the (anti)quarks in the plasma during equilibration by the gluon field. We assume generally accepted T(${\mathrm{\ensuremath{\mu}}}_{\mathit{q}}$=0) and ${\mathrm{\ensuremath{\mu}}}_{\mathit{q}}$(T=0) values to construct a phase curve, defining an approximate lower limit of the ideal QGP phase. We express the strange particle ratios as function of ${\mathrm{\ensuremath{\mu}}}_{\mathit{q}}$ and T along this curve and predict quantitatively their minimum QGP values. We analyze the NA36 and WA85 CERN experiments and obtain the quarkchemical potentials, ${\mathrm{\ensuremath{\mu}}}_{\mathit{q}}$, ${\mathrm{\ensuremath{\mu}}}_{\mathit{s}}$ and the chemical equilibration, ${\ensuremath{\gamma}}_{\mathit{s}}$. The gluon sector, providing the q\ifmmode\bar\else\textasciimacron\fi{}'s, is necessary for the correct and consistent estimation of these quantities and prediction of all strange particle ratios. We put forward that the values of T, ${\mathrm{\ensuremath{\mu}}}_{\mathit{q}}$, ${\mathrm{\ensuremath{\mu}}}_{\mathit{s}}$, and ${\ensuremath{\gamma}}_{\mathit{s}}$ are the only significant quantities determining a possible phase transition, not the magnitude of any strange particle ratio, as previously proclaimed. We find that the 200 GeV/nucleon $^{32}\mathrm{induced}$ interactions at midrapidity may have approached the ideal QGP phase to within about 60%.