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Brown-dwarfs are substellar objects with masses intermediate between planets and stars within about 13-80Mjup. While isolated BDs are most likely produced by gravitational collapse in molecular clouds down to masses of a few Mjup, a non-negligible fraction of low-mass companions might be formed through the planet formation channel in protoplanetary disks. The upper mass limit of objects formed within disks is still observationally unknown, the main reason being the strong dearth of BD companions at orbital periods shorter than 10 years, a.k.a. the BD desert. To address this question, we aim at determining the best statistics of secondary companions within the 10-100Mjup range and within 10 au from the primary star, while minimising observational bias. We made an extensive use of the RV surveys of FGK stars below 60pc distance to the Sun and in the northern hemisphere performed with the SOPHIE spectrograph at the Observatoire de Haute-Provence. We derived the Keplerian solutions of the RV variations of 54 sources. Public astrometric data of the Hipparcos and Gaia missions allowed constraining the mass of the companion for most sources. We introduce GASTON, a new method to derive inclination combining RVs Keplerian and astrometric excess noise from Gaia DR1. We report the discovery of 12 new BD candidates. For 5 of them, additional astrometric data led to revise their mass in the M-dwarf regime. Among the 7 remaining objects, 4 are confirmed BD companions, and 3 others are likely in this mass regime. We also report the detection of 42 M-dwarfs within 90Mjup-0.52Msun. The resulting Msin(i)-P distribution of BD candidates shows a clear drop in the detection rate below 80-day orbital period. Above that limit, the BD desert reveals rather wet, with a uniform distribution of the Msin(i). We derive a minimum BD-detection frequency around Solar-like stars of 2.0+/-0.5%., Comment: 51 pages, 20 figures, 16 tables