brightest supernovae at the peak of their light curves and $\Delta m<0$ is a free parameter defining the magnitude gap between lensed and non-lensed supernovae. Absolute magnitudes and K-corrections can be calculated from spectral templates of the assumed reference class of bright supernovae, while the redshift of the apparent host galaxy can be estimated from existing photometric data from wide-field surveys. Since only rare cases of supernovae are brighter than SNe Ia, e.g. superluminous supernovae, it is reasonable to use type Ia as the reference class of bright supernovae. Like @Gold2017, we assume a mean peak absolute magnitude of $-19.3$ in the $B$ band.

The choice of the parameter $\Delta m$ is dictated by a trade-off between the completeness and the contamination of the selected lensed supernova candidates. As a base model, we use $\Delta m=-0.7$ required for distinguishing between the brightest non-lensed type Ia supernovae and gravitationally lensed supernovae [@Gold2017]. We expect that the assumed magnitude gap is a sufficiently conservative choice from the point of view of minimizing the false positive rate. However, one has to bear in mind that rare luminous supernovae brighter than $-20$ in the $B$ band inevitably will be confused with lensed supernovae in 