  We explore the cosmological implications of 7 deep survey fields observed at
the Berkeley-Illinois-Maryland Association (BIMA) Array with 30 GHz receivers.
These observations probe the Cosmic Microwave Background anisotropy on scales
corresponding to l=5500, and an earlier analysis of these data detected no
galaxy clusters. We use numerical cluster simulations and mock observations to
characterize the cluster detection efficiency for each of the BIMA fields. With
these detection efficiencies we derive constraints on the cosmological
parmaters OmegaM and sigma8, ruling out those models which overproduce galaxy
clusters. Using only these seven BIMA fields, we calculate a 2sigma upper limit
of sigma8 < 1.00OmegaM**(-0.43OmegaM-0.22) for flat models with 0.1<OmegaM<1.
When the power spectrum of density fluctuations is COBE normalized, we find
OmegaM < 0.63 at 95% confidence level for flat models. This constraint includes
our estimate of the large uncertainties in the SZE flux-virial mass
relationship as well as published uncertainties in the Hubble parameter, the
COBE power spectrum normalization and the primordial power spectrum index. In
addition, we account for the effects of sample variance. Thus, we conclude that
the non-detections are to be expected in a low OmegaM universe, given the
sensitivity and solid angle of the deepest SZE survey to date.
