tokens: only increases the number count by ∼0.01. There is a dependence of number count on the cadence, and it can be used to set the actual cadence. Although the cadence of the main survey is already fixed at 27d on average, number counts in the ADS increase until the cadence reaches a few times 10 d and are more or less flat thereafter. Consequently, number counts in the ADS are not sensitive to cadence above 1–2 months. Also, we note that with just two pointings one year apart in DD fields, our number counts could be contaminated by false positives due to AGNs. However, these objects can be disentangled from high- z SNe to some degree because their luminosities are typically higher than those of SNe and fluctuate stochastically by about an order of magnitude over the time-scales that SN LCs evolve. In contrast, SNe brighten and then fade by a larger factor. 3.4.3 Scattering/absorption We treat attenuation of flux due to Ly α scattering with the model of Madau ( 1995 ) at z 6 and with Gunn Peterson ( 1965 ) for z > 6. The errors in Madau ( 1995 ) can be large but λ Ly α is only redshifted through the i band and of the z band at z 6. The large uncertainties in Madau ( 1995 ) therefore have little impact on our results because of the low numbers of counts in the i band and because they only affect part of the z band. High-redshift SNe might be obscured by dust at lower galactic altitudes. However, this will likely have little effect on the number of detections since this region of the sky is not covered by the WFD. There may also be extinction in the host galaxies. This extinction depends on the metallicity. Pop III galaxies are believed to be free of dust, so they would not obscure explosions (Rydberg et al. 2017 ). Dust in the host galaxies of Pop II SNe may dim them but the extinction is expected to be weak because they are being observed in rest-frame UV. At z ∼ 5–7 the host galaxies also likely have low metallicities and less dust. 3.4.4 Lensing model For the systemic errors due to the lensing models, we use the factor two, as mentioned in Section 2.4 , as an to denote the possible errors in the predicted numbers of SNe. A source of potentially large uncertainty in our lensing models is the fraction of the sky with 1 μ 2 (Section 2.4 ). The interpolation we use yields a rather severe lower limit because at μ = 1 it returns a lensed area that is just a few per cent of the sky. As a simple test of how robust our counts are with respect to this interpolation we have done it with a second-degree polynomial in the log 10 –log 10 plane as well. As constraints we use f (μ = 1) = 1 and f (μ = 2) = f 2 , where f(μ) is the fraction of the sky magnified by at least μ. The slope of the interpolation between μ = 2 and μ = 3 is set equal to the derivative of the polynomial. None of the counts in the WFD change because detections there always require magnifications greater than two, as seen in Table 1 . In the ADS the use of this interpolation adds on average
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O B-Citation I-Citation I-Citation I-Citation O B-Formula I-Formula O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Formula I-Formula I-Formula O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O O B-Formula I-Formula O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O