We propose an experiment intended for search for an admixture of sterile neutrino with mass m$_s$ in the range of 1-8 keV that may be detected as specific distortion of the electron energy spectrum during tritium decay. The distortion is spread over large part of the spectrum so to reveal it one can use a detector with relatively poor (near 10-15%) energy resolution. A classic proportional counter is a simple natural choice for a tritium $beta$-decay detector. The method we are proposing is original in two respects. First, the counter is produced as a whole from fully-fused quartz tube allowing to measure current pulse directly from anode while providing high stability for a long time. Second, a modern digital acquisition technique can be used in measurements at ultrahigh count rate - up to 10$^6$ Hz. As a result an energy spectrum of tritium electrons containing up to 10$^{12}$ counts may be collected in a month of live time measurements. Due to high statistics an upper limit down to 10$^{-3}$..10$^{-5}$ can be put on sterile neutrino mixing at 95% CL for m$_s$ in the range of 1-8 keV, that will be 1..2 orders of magnitude better then bounds published up to now.
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