cone up to redshift $z=3$ with supernovae. In order to reduce shot noise, we artificially increase the supernovae rate by a factor of $5\times10^{5}$. The actual detection rate is then retrieved by scaling down the counts by the same factor. In order to save computational time (driven primarily by lensing computations), we discard all supernovae at angular distances larger than $4\theta_{E}$. These supernovae are typically too far from the lenses to be multiply imaged or strongly magnified. Our choice of a maximum redshift for the lenses and the supernovae allows us to determine detection rates of strongly lensed supernovae for limiting magnitudes up to 26, which is around 2 mag deeper than the envisaged depth for the LSST.

For every lens-supernova pair we calculate all basic lensing properties, i.e. image multiplicity, magnifications, positions of the images and time delays. The lensing equations are solved numerically using the publicly available code for lensing calculations, *glafic* [@Ogu2010]. When calculating time dependent apparent magnitudes, we take into account both the effects of magnification and time delay determined for every image.

Once the complete Monte Carlo sample of strongly lensed supernovae is computed, we can employ different detection criteria and thus determine the number 