of bright supernovae sets a relatively conservative detection threshold. However, as we shall see, the higher volumetric rates of core-collapse supernovae can compensate their lower luminosities leading to even higher discovery rates than for type Ia.

Hybrid approach
---------------

As we shall see in Section 4, the two methods described perform very differently. The methods are complementary in many respects in that they maximize their efficiencies in different ranges of survey depth. This provides motivation for considering a third approach which combines the ideas underlying the two techniques. Here, a transient is classified as a lensed supernova candidate if at least one of the two methods identifies it as a potential lensed supernova.

Simulations
===========

We employ a Monte Carlo approach to compute the expected number of observed strongly lensed supernovae. The method relies on drawing random realizations of lens galaxies and supernovae in a light cone, and counting strong lensing events which satisfy certain detection conditions.

Lens galaxies
-------------

Motivated by its success in modeling multiply imaged QSOs, we assume that the mass distribution in the lens galaxies is adequately represented by a Singular Isothermal Ellipsoid (SIE) model [@Kor1994] in which the convergence $\kappa$ is given by: $$\begin{aligned}
\kappa(x,y) 