We report new nearby L and late-M dwarfs (d_phot <= 30 pc) discovered in our search for nearby ultracool dwarfs (I-J >= 3.0, later than M8.0) at low Galactic latitude (|b| < 15 degr) over 4,800 square degrees in the DENIS database. We used late-M (>=M8.0), L, and T dwarfs with accurate trigonometric parallaxes to calibrate the M_J versus I-J colour-luminosity relation. The resulting photometric distances have standard errors of ~15%, which we used to select candidates d_phot <= 30 pc. We measured proper motions from multi-epoch images found in the public archives ALADIN, DSS, 2MASS, DENIS, with at least three distinct epochs and time baselines of 10 to 21 years. We then used a Maximum Reduced Proper Motion cutoff to select 28 candidates as ultracool dwarfs (M8.0--L8.0) and to reject one as a distant red star. No T dwarf candidates were found in this search which required an object to be detected in all three DENIS bands. Our low-resolution optical spectra confirmed that 26 of them were indeed ultracool dwarfs, with spectral types from M8.0 to L5.5. Two contaminants and one rejected by the Maximum Reduced Proper Motion cutoff were all reddened F-K main sequence stars. 20 of these 26 ultracool dwarfs are new nearby ultracool dwarf members, three L dwarfs within 15 pc with one L3.5 at only ~10 pc. We determine a stellar density of bar{Phi}_J cor=(1.64 +- 0.46).10^{-3} dwarfs pc^{-3} mag^{-1} over 11.1 <= M_J <= 13.1 based on that sample of M8--L3.5 ultracool dwarfs. Our ultracool dwarf density value is in good agreement with the Cruz et al. measurement of the ultracool dwarf density at high Galactic latitude.
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