We have been conducting a systematic search for brown dwarfs around solar neighborhood G&K 
dwarfs, using NACO in its Simultaneous Differential Imaging mode. We took advantage of the 
CORALIE planet search radial velocity survey, to select a subsample of 36 G&K dwarfs out of 
1600 inside 50 parsecs. These 36 stars display radial velocity drifts compatible with a 
substellar companions in the separation range accessible to NACO+SDI, and that are not known 
as long period spectroscopic or visual binaries. We found 16 obvious stellar companions 
(mostly late M type dwarfs). At this stage of the data processing, we do not directly detect 
the companions on the remaining 20 stars, pointing that these companions are either massive 
planets or low mass brown dwarfs. We will present here the results of our program and new 
constraints on the brown dwarf desert in the separation range from 1 to 100 AU.