luminosities in the $B$ band of the different types of supernovae considered in our study. Normalizations of the distributions are proportional to the local volumetric rates of the correposnding supernova classes. The green dashed curve shows an alternative model for type Ia supernovae with with a tail accounting for low-luminosity supernovae.[]{data-label="abs_lum"}](abs_lum){width="48.00000%"}

We calculate light curves and K-corrections of simulated type Ia supernovae (normal branch) using a time series of spectral templates computed by @Nug2002. Following @Gold2017, we assume that the absolute magnitude is normally distributed with a mean of $-19.3$ in the $B$ band and a scatter of $0.2$. We also check the impact of using a more realistic distribution with 3 times longer Gaussian tail at low luminosities accounting for faint supernovae in volume-limited samples [see e.g. @Li2011; @Gold2017]. For core collapse supernovae, we consider types Ib/c, IIP, IIL and IIn, assuming that their relative contributions to the total number density of core collapse supernovae are independent of redshift and constrained by low-redshift observations resulting in 16, 49, 9 and 5 per cent respectively for Ib/c, IIP, IIL and IIn [@Gra2017; @Li2011]. We realize light curves of the four supernova subclasses using spectral templates from a compilation which is 