of type Ia supernovae expected in the apparent host (lens) galaxy ($\Delta m=-0.7$ for the base model). For the image multiplicity method, discovery rates depend on the minimum number of detectable images. The solid and dashed curves compare the two cases for which at least three (base model) or two images are detectable for quads and cusps. The red dashed-dotted curves shows the impact of accounting for the possible low-luminosity tail in the luminosity function $d\textrm{n}_{\rm SNIa}/dM_{\rm B}$ of type Ia supernovae (see the green dashed curve in Fig. \[abs\_lum\]) on the expected discovery rates. []{data-label="sn_rate_effects"}](effect-of-parameters){width="48.00000%"}

The performance of the magnification method depends on the choice of the number of images that contribute to the total flux in the observations. The red band in Fig. \[yields\_comparison\] shows the expected range of the rates modulated by this effect. The upper limit corresponds to detections based on flux integrated over all images, whereas the lower limit is expected for detections based on flux solely from the brightest image. The average ratio between the upper and lower limits is 2, with a very weak dependence on survey depth and filters.

The apparent differences between detection rates from the two main methods reflect the 