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The BL Lac object H1426+428 ($zequiv 0.129$) is an established source of TeV $gamma$-rays and detections of these photons from this object also have important implications for estimating the Extragalactic Background Light (EBL) in addition to the und erstanding of the particle acceleration and $gamma$-ray production mechanisms in the AGN jets. We have observed this source for about 244h in 2004, 2006 and 2007 with the TACTIC $gamma$-ray telescope located at Mt. Abu, India. Detailed analysis of these data do not indicate the presence of any statistically significant TeV $gamma$-ray signal from the source direction. Accordingly, we have placed an upper limit of $leq1.18times10^{-12}$ $photons$ $cm^{-2}$ $s^{-1}$ on the integrated $gamma$-ray flux at 3$sigma$ significance level.
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