The Next Generation Fornax Survey (NGFS): III. Revealing the Spatial
  Substructure of the Dwarf Galaxy Population inside half of Fornax's Virial
  Radius
  We report the discovery of 271 previously undetected dwarf galaxies in the
outer Fornax cluster regions at radii $r_{\rm vir}/4<\!r\!<r_{\rm vir}/2$ using
data from the Next Generation Fornax Survey (NGFS) with deep coadded $u'$, $g'$
and $i'$ images obtained with Blanco/DECam at Cerro Tololo Interamerican
Observatory. From the 271 dwarf candidates we find 39 to be nucleated. Together
with our previous study of the central Fornax region, the new dwarfs detected
with NGFS data are 392, of which 56 are nucleated. The total Fornax dwarf
galaxy population from NGFS and other catalogs rises, therefore, to a total of
643 with 181 being nucleated, yielding an overall nucleation fraction of
$28\%$. The absolute $i'$-band magnitudes for the outer NGFS dwarfs are in the
range $-18.80\le\,M_{i'}\le\,-8.78$ with effective radii $r_{{\rm
eff},i'}\,=\,0.18-2.22$ kpc and an average Sersic index $\langle
n\rangle_{i'}\,=\,0.81$. Non-nucleated dwarfs are found to be fainter and
smaller by $\Delta\langle M_{i'}\rangle\!=\!2.25$ mag and $\Delta\langle
r_{{\rm eff},i'}\rangle\!=\!0.4$ kpc than the nucleated dwarfs. We demonstrate
a significant clustering of dwarf galaxies on scales $\lesssim\!100$ kpc, and
projected surface number density profile estimates, $\Sigma_N(r)$, show a
concentration of dwarfs in the Fornax core region within $r\!\sim\!350$ kpc.
$\Sigma_N(r)$ has a flat distribution up to $\sim\!350$ kpc, beyond which it
declines for the non-nucleated dwarfs. The nucleated dwarfs have a steeper
$\Sigma_N(r)$ distribution, being more concentrated towards NGC 1399 and
decreasing rapidly outwards. This is the first time the transition from cluster
to field environment has been established for the very faint dwarf galaxy
population with robust sample statistics.
