  We present a map of the total intrinsic reddening across ~34 deg$^{2}$ of the
Small Magellanic Cloud (SMC) derived using optical ($ugriz$) and near-infrared
(IR; $YJK_{\mathrm{s}}$) spectral energy distributions (SEDs) of background
galaxies. The reddening map is created using a subsample of 29,274 galaxies
with low levels of intrinsic reddening based on the LePhare $\chi^{2}$
minimisation SED-fitting routine. We find statistically significant enhanced
levels of reddening associated with the main body of the SMC compared with
regions in the outskirts [$\Delta E(B-V)\simeq 0.3$ mag]. A comparison with
literature reddening maps of the SMC shows that, after correcting for
differences in the volume of the SMC sampled, there is good agreement between
our results and maps created using young stars. In contrast, we find
significant discrepancies between our results and maps created using old stars
or based on longer wavelength far-IR dust emission that could stem from biased
samples in the former and uncertainties in the far-IR emissivity and the
optical properties of the dust grains in the latter. This study represents one
of the first large-scale categorisations of extragalactic sources behind the
SMC and as such we provide the LePhare outputs for our full sample of ~500,000
sources.
