  We present the Arecibo Dual-Beam Survey (ADBS), a "blind" 21cm survey for
galaxies. The ADBS is the largest to date with the Arecibo radio telescope. We
were able to achieve an rms sensitivity of 3-4 mJy in only 7 seconds. The ADBS
covers substantially more volume than the Spitzak & Schneider (1998) and the
Zwaan et al. (1997) surveys. It is surpassed by the Parkes HIPASS survey
(Kilborn et al. 1999) but has much better angular resolution and sensitivity.
We will discuss the HI sample and our efforts to quantify the completeness and
reliability.
  This is the first survey to use synthetic sources to establish the relation
between the flux, line width, and completeness of the survey. An empirical
understanding of these quantities is vital to the determination of the mass
function. Even if we do not understand all of the reasons why we do not detect
galaxies, the empirical understanding allows us to account for them properly.
  In addition to the more general discussion of the ADBS survey, we will
discuss galaxies which have large ratios of HI mass to optical area and
probably have extended HI disks. We detect a much higher percentage of these
high HI mass to optical area galaxies than are seen in optical surveys
indicating that optical surveys miss these galaxies. Among these galaxies are
also 7 galaxies with HI masses < 10^8 M_sun. Based on the mass function of
Schneider & Rosenberg (this volume), the low mass galaxies are an important
part of the general galaxy population.
