  The frequency and properties of multiple star systems offer powerful tests of
star formation models. Multiplicity surveys over the past decade have shown
that binary properties vary strongly with mass, but the functional forms and
the interplay between frequency and semimajor axis remain largely
unconstrained. We present the results of a large-scale survey of multiplicity
at the bottom of the IMF in several nearby young associations, encompassing 78
very low mass members observed with Keck laser guide star adaptive optics. Our
survey confirms the overall trend observed in the field for lower-mass binary
systems to be less frequent and more compact, including a null detection for
any substellar binary systems with separations wider than ~7 AU. Combined with
a Bayesian re-analysis of existing surveys, our results demonstrate that the
binary frequency and binary separations decline smoothly between masses of 0.5
Msun and 0.02 Msun, though we can not distinguish the functional form of this
decline due to a degeneracy between the total binary frequency and the mean
binary separation. We also show that the mass ratio distribution becomes
progressively more concentrated at q~1 for declining masses, though a small
number of systems appear to have unusually wide separations and low mass ratios
for their mass. Finally, we compare our results to synthetic binary populations
generated by smoothed particle hydrodynamic simulations, noting the
similarities and discussing possible explanations for the differences.
