  The HOSTS (Hunt for Observable Signatures of Terrestrial Systems) survey
searches for dust near the habitable zones (HZs) around nearby, bright main
sequence stars. We use nulling interferometry in N band to suppress the bright
stellar light and to probe for low levels of HZ dust around the 30 stars
observed so far. Our overall detection rate is 18%, including four new
detections, among which are the first three around Sun-like stars and the first
two around stars without any previously known circumstellar dust. The inferred
occurrence rates are comparable for early type and Sun-like stars, but decrease
from 60 (+16/-21)% for stars with previously detected cold dust to 8 (+10/-3)%
for stars without such excess, confirming earlier results at higher
sensitivity. For completed observations on individual stars, our sensitivity is
five to ten times better than previous results. Assuming a lognormal excess
luminosity function, we put upper limits on the median HZ dust level of 13
zodis (95% confidence) for a sample of stars without cold dust and of 26 zodis
when focussing on Sun-like stars without cold dust. However, our data suggest
that a more complex luminosity function may be more appropriate. For stars
without detectable LBTI excess, our upper limits are almost reduced by a factor
of two, demonstrating the strength of LBTI target vetting for future exo-Earth
imaging missions. Our statistics are so far limited and extending the survey is
critical to inform the design of future exo-Earth imaging surveys.
