  The "ALFA Ultra Deep Survey" (AUDS) is an ongoing 21-cm spectral survey with
the Arecibo 305m telescope. AUDS will be the most sensitive blind survey
undertaken with Arecibo's 300 MHz Mock spectrometer. The survey searches for
21-cm HI line emission at redshifts between 0 and 0.16. The main goals of the
survey are to investigate the HI content and probe the evolution of HI gas
within that redshift region. In this paper, we report on a set of precursor
observations with a total integration time of 53 hours. The survey detected a
total of eighteen 21-cm emission lines at redshifts between 0.07 and 0.15 in a
region centered around ra~0:00h, dec= 15:42deg. The rate of detection is
consistent with the one expected from the local HI mass function. The derived
relative HI density at the median redshift of the survey is
rho_HI[z=0.125]=(1.0+/-0.3)*rho_0, where rho_0 is the HI density at zero
redshift.
