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.
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