for the image multiplicity method increase exponentially with limiting magnitudes in a range between 24 and 26, whereas the rates from the magnification method become constant.

Both methods are expected to find comparable numbers of lensed type Ia supernovae at limiting magnitudes between $23.0$ in the $g$ band to $23.8$ in the $y$ band. The lensed supernova samples returned by the two methods happen to be only weakly overlapping; therefore, combining both detection criteria is expected to increase the yields, especially at intermediate limiting magnitudes. This is demonstrated by the solid curves which show detection rates for the hybrid method which identifies strongly lensed supernovae either as highly magnified or multiply imaged transients. The hybrid method maximizes supernova yields at all limiting magnitudes. Unsurprisingly, it follows closely the rates from the magnification method at $X_{\rm lim}\lesssim21$ and the image multiplicity technique at $X_{\rm lim}\gtrsim24$.

![Sensitivity of detecting lensed type Ia supernova in the $z$ band to parameters and conditions defining detection criteria of the two methods based on selecting highly magnified (red curves) or multiply imaged supernovae (green curves). The parameter $\Delta m$ is a minimum enhancement of the apparent brightness due to lensing magnification relative to the mean magnitude 