  The Arecibo Ultra Deep Survey (AUDS) is a blind HI survey aimed at detecting
galaxies beyond the local Universe in the 21-cm emission line of neutral
hydrogen (HI). The Arecibo $L$-band Feed Array (ALFA) was used to image an area
of 1.35~deg$^2$ to a redshift depth of 0.16, using a total on-source
integration time of over 700 hours. The long integration time and small
observation area makes it one of the most sensitive HI surveys, with a noise
level of $\sim 75$~$\mu$Jy per 21.4~kHz (equivalent to 4.5~km~s$^{-1}$ at
redshift $z=0$). We detect 247 galaxies in the survey, more than doubling the
number already detected in AUDS60. The mass range of detected galaxies is
$\log(M_{\rm HI}~[h_{70}^{-2}{\rm M}_\odot]) = 6.32 - 10.76$. A modified
maximum likelihood method is employed to construct an HI mass function (HIMF).
The best fitting Schechter parameters are: low-mass slope $\alpha = -1.37 \pm
0.05$, characteristic mass $\log(M^*~[h_{70}^{-2}{\rm M}_\odot]) = 10.15 \pm
0.09$, and density $\Phi_* = (2.41 \pm 0.57) \times 10^{-3}
h_{70}^3$~Mpc$^{-3}$~dex$^{-1}$. The sample was divided into low and high
redshift bins to investigate the evolution of the HIMF. No change in low-mass
slope $\alpha$ was measured, but an increased characteristic mass $M^*$, was
noted in the higher-redshift sample. Using Sloan Digital Sky Survey (SDSS) data
to define relative galaxy number density, the dependence of the HIMF with
environment was also investigated in the two AUDS regions. We find no
significant variation in $\alpha$ or $M^*$. In the surveyed region, we measured
a cosmic HI density $\Omega_{\rm HI} = (3.55 \pm 0.30) \times 10^{-4}
h_{70}^{-1}$. There appears to be no evolutionary trend in $\Omega_{\rm HI}$
above $2\sigma$ significance between redshifts of 0 and 0.16.
