Study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mover accent="true"><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mo>+</mml:mo></mml:msup></mml:math> at center-of-mass energies from 3.49 to 3.67 GeV

Using data samples of ${e}^{+}{e}^{\ensuremath{-}}$ collisions collected with the BESIII detector at eight center-of-mass energy points between 3.49 and 3.67 GeV, corresponding to an integrated luminosity of $670\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$, we present the upper limits of Born cross sections and the effective form factor for the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}{\overline{\mathrm{\ensuremath{\Omega}}}}^{+}$. A fit to the cross sections using a perturbative QCD-derived energy-dependent function shows no significant threshold effect. The upper limit on the measured effective form factor is consistent with a theoretical prediction within the uncertainty of $1\ensuremath{\sigma}$. These results provide new experimental information on the production mechanism of $\mathrm{\ensuremath{\Omega}}$.