  The ALMA SPECtroscopic Survey in the {\it Hubble} Ultra Deep Field is an ALMA
large program that obtained a frequency scan in the 3\,mm band to detect
emission lines from the molecular gas in distant galaxies. We here present our
search strategy for emission lines and continuum sources in the HUDF. We
compare several line search algorithms used in the literature, and critically
account for the line-widths of the emission line candidates when assessing
significance. We identify sixteen emission lines at high fidelity in our
search. Comparing these sources to multi-wavelength data we find that all
sources have optical/infrared counterparts. Our search also recovers candidates
that have lower significance that can be used statistically to derive, e.g. the
CO luminosity function. We apply the same detection algorithm to obtain a
sample of six 3 mm continuum sources. All of these are also detected in the 1.2
mm continuum with optical/near-infrared counterparts. We use the continuum
sources to compute 3 mm number counts in the sub-mJy regime, and find them to
be higher by an order of magnitude than expected for synchrotron-dominated
sources. However, the number counts are consistent with those derived at
shorter wavelengths (0.85--1.3\,mm) once extrapolating to 3\,mm with a dust
emissivity index of $\beta=1.5$, dust temperature of 35\,K and an average
redshift of $z=2.5$. These results represent the best constraints to date on
the faint end of the 3 mm number counts.

Astrophysics of Galaxies