| A new powerful method for deep radio surveys in the 21 cm line is introduced. The method is capable of collecting large amounts of data in a very efficient way and, analyzing it accurately and quickly compared to previous methods. The method is applied to two HI surveys using the Arecibo Telescope to determine the low and high mass ends of the HI-mass function for nearby galaxies. The first one, which we call the Sensitive HI Survey, was designed to place sensitive limits on the space density of small HI-mass clouds or dwarf galaxies. The implication of the Sensitive HI Survey is that there is not enough neutral gas hidden in low-surface-brightness galaxies or intergalactic clouds to substantially increase the integral amount of HI in the nearby Universe over that contained in optically-selected galaxies. The second survey was designed to discover huge HI-rich galaxies; in order to maximize the survey volume, probed by each telescope beam area, the receiving system was tuned to search for HI emission for galaxies in the redshift interval 19,000 km s{dollar}sp{lcub}-1{rcub}{dollar} to 28,000 km s{dollar}sp{lcub}-1{rcub}{dollar}. Since no new "Malin 1 type" galaxies (M{dollar}sb{lcub}HI{rcub} > 5times 10sp{lcub}10{rcub}Msb{lcub}odot{rcub}){dollar} were discovered in 16,500 Mpc{dollar}sp3{dollar}, the survey sets an upper limit for the number density of objects with HI-masses greater than 10{dollar}sp{lcub}10.5{rcub}Msb{lcub}odot{rcub}{dollar} as {dollar}1.8times 10sp{lcub}-4{rcub}{dollar} Mpc{dollar}sp{lcub}-3{rcub}{dollar} with a 95% confidence level. |
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