  We report the discovery of 158 previously undetected dwarf galaxies in the
Fornax cluster central regions using a deep coadded $u, g$ and $i$-band image
obtained with the DECam wide-field camera mounted on the 4-meter Blanco
telescope at the Cerro Tololo Interamerican Observatory as part of the {\it
Next Generation Fornax Survey} (NGFS). The new dwarf galaxies have
quasi-exponential light profiles, effective radii $0.1\!<\!r_e\!<\!2.8$ kpc and
average effective surface brightness values $22.0\!<\!\mu_i\!<\!28.0$ mag
arcsec$^{-2}$. We confirm the existence of ultra-diffuse galaxies (UDGs) in the
Fornax core regions that resemble counterparts recently discovered in the Virgo
and Coma galaxy clusters.~We also find extremely low surface brightness NGFS
dwarfs, which are several magnitudes fainter than the classical UDGs. The
faintest dwarf candidate in our NGFS sample has an absolute magnitude of
$M_i\!=\!-8.0$\,mag. The nucleation fraction of the NGFS dwarf galaxy sample
appears to decrease as a function of their total luminosity, reaching from a
nucleation fraction of $>\!75\%$ at luminosities brighter than
$M_i\!\simeq\!-15.0$ mag to $0\%$ at luminosities fainter than
$M_i\!\simeq\!-10.0$ mag. The two-point correlation function analysis of the
NGFS dwarf sample shows an excess on length scales below $\sim\!100$ kpc,
pointing to the clustering of dwarf galaxies in the Fornax cluster core.
