Nearby supernova rates from the Lick Observatory Supernova Search - I. The methods and data base

This is the first paper of a series in which we present new measurements of\nthe observed rates of supernovae (SNe) in the local Universe, determined from\nthe Lick Observatory Supernova Search (LOSS). We have obtained 2.3 million\nobservations of 14,882 sample galaxies over an interval of 11 years (March 1998\nthrough Dec. 2008). We considered 1036 SNe detected in our sample and used an\noptimal subsample of 726 SNe (274 SNe~Ia, 116 SNe~Ibc, 324 SNe~II) to determine\nour SN rates. This is the largest and most homogeneous set of nearby SNe ever\nassembled for this purpose, and ours is the first local SN rate analysis based\non CCD imaging and modern image-subtraction techniques. In this paper, we lay\nthe foundation of the study. We derive the recipe for the control-time\ncalculation for SNe with a known luminosity function, and provide details on\nthe construction of the galaxy and SN samples used in the calculations.\nCompared with a complete volume-limited galaxy sample, our sample has a deficit\nof low-luminosity galaxies but still provides enough statistics for a reliable\nrate calculation. There is a strong Malmquist bias, so the average size\n(luminosity or mass) of the galaxies increases monotonically with distance, and\nthis trend is used to showcase a correlation between SN rates and galaxy sizes.\nVery few core-collapse SNe are found in early-type galaxies, providing strong\nconstraints on the amount of recent star formation within these galaxies. The\nsmall average observation interval ($\\sim 9$ days) of our survey ensures that\nour control-time calculations can tolerate a reasonable amount of uncertainty\nin the luminosity functions of SNe. We perform Monte Carlo simulations to\ndetermine the limiting magnitude of each image and the SN detection efficiency\nas a function of galaxy Hubble type ... (abridged)\n