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Strongly lensed supernovae can be detected as multiply imaged or highlymagnified transients. In order to compare the performances of these twoobservational strategies, we calculate expected discovery rates as a functionof survey depth in five grizy filters and for different classes of supernovae(Ia, IIP, IIL, Ibc and IIn). We find that detections via magnification is theonly effective strategy for relatively shallow pre-LSST surveys. For surveydepths about the LSST capacity, both strategies yield comparable numbers oflensed supernovae. Supernova samples from the two methods are to a large extentindependent and combining them increases detection rates by about 50 per cent.While the number of lensed supernovae detectable via magnification saturates atthe limiting magnitudes of LSST, detection rates of multiply imaged supernovastill go up drastically at increasing survey depth. Comparing potentialdiscovery spaces, we find that lensed supernovae found via image multiplicityexhibit longer time delays and larger image separations making them moresuitable for cosmological constraints than their counterparts found viamagnification.  We find that the ZTF will find about 2 type Ia and 4 core-collapse lensedsupernovae per year at a limiting magnitude of 20.6 in the r band. Applying ahybrid method which combines searching for highly magnified or multiply imagedtransients, we find that LSST will detect 89 type Ia and 254 core-collapselensed supernovae per year. In all cases, lensed core-collapsed supernovae willbe dominated by type IIn supernovae contributing to 80 per cent of the totalcounts, although this prediction relies quite strongly on the adopted spectraltemplates for this class of supernovae. Revisiting the case of the lensedsupernova iPTF16geu, we find that it is consistent within the 2\sigma contoursof predicted redshifts and magnifications for the iPTF survey.

Magnified or multiply imaged? - Search strategies for gravitationally lensed supernovae in wide-field surveys