We have carried out a sensitive high-latitude (|b| > 15deg.) HI 21cm-line absorption survey towards 102 sources using the GMRT. With a 3-sigma detection limit in optical depth of ~0.01, this is the most sensitive HI absorption survey. We detected 126 absorption features most of which also have corresponding HI emission features in the Leiden Dwingeloo Survey of Galactic neutral Hydrogen. The histogram of random velocities of the absorption features is well-fit by two Gaussians centered at V(lsr) ~ 0 km/s with velocity dispersions of 7.6 +/- 0.3 km/s and 21 +/- 4 km/s respectively. About 20% of the HI absorption features form the larger velocity dispersion component. The HI absorption features forming the narrow Gaussian have a mean optical depth of 0.20 +/- 0.19, a mean HI column density of (1.46 +/- 1.03) X 10^{20} cm^{-2}, and a mean spin temperature of 121 +/- 69 K. These HI concentrations can be identified with the standard HI clouds in the cold neutral medium of the Galaxy. The HI absorption features forming the wider Gaussian have a mean optical depth of 0.04 +/- 0.02, a mean HI column density of (4.3 +/- 3.4) X 10^{19} cm^{-2}, and a mean spin temperature of 125 +/- 82 K. The HI column densities of these fast clouds decrease with their increasing random velocities. These fast clouds can be identified with a population of clouds detected so far only in optical absorption and in HI emission lines with a similar velocity dispersion. This population of fast clouds is likely to be in the lower Galactic Halo.
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