In this paper we present a catalogue of 11745 brown dwarfs with spectral types ranging from L0 to T9, photometrically classified using data from the Dark Energy Survey (DES) year 3 release matched to the Vista Hemisphere Survey (VHS) DR3 and Wide-field Infrared Survey Explorer (WISE) data, covering 2400deg2 up to iAB= 22. The classification method follows the same phototype method previously applied to SDSS-UKIDSS-WISE data. The most significant difference comes from the use of DES data instead of SDSS, which allow us to classify almost an order of magnitude more brown dwarfs than any previous search and reaching distances beyond 400 pc for the earliest types. Next, we also present and validate the GalmodBD simulation, which produces brown dwarf number counts as a function of structural parameters with realistic photometric properties of a given survey. We use this simulation to estimate the completeness and purity of our photometric LT catalogue down to iAB= 22, as well as to compare to the observed number of LT types. We put constraints on the thin disc scale height for the early L (L0L3) population to be around 450 pc, in agreement with previous findings. For completeness, we also publish in a separate table a catalogue of 20863M dwarfs that passed our colour cut with spectral types greater than M6. Both the LT and the late M catalogues are found at DES release page https://des.ncsa.illinois.edu/releases/other/y3-mlt.