  Small planets are common around late-M dwarfs and can be detected through
highly precise photometry by the transit method. Planets orbiting nearby stars
are particularly important as they are often the best-suited for future
follow-up studies. We present observations of three nearby M-dwarfs referred to
as EIC-1, EIC-2, and EIC-3, and use them to search for transits and set limits
on the presence of planets. On most nights our observations are sensitive to
Earth-sized transiting planets, and photometric precision is similar to or
better than TESS for faint late-M dwarfs of the same magnitude (I=15 mag). We
present our photometry and transit search pipeline, which utilizes simple
median detrending in combination with transit least squares based transit
detection (Hippke & Heller 2019).For these targets, and transiting planets
between one and two Earth radii, we achieve an average transit detection
probability of 60% between periods of 0.5 and 2 days, 30% between 2 and 5
days,and 10% between 5 and 10 days. These sensitivities are conservative
compared to visual searches.
