  We have used Monte Carlo simulation techniques and published radial velocity
surveys to constrain the frequency of very low-mass star (VLMS) and brown dwarf
(BD) binary systems and their separation (a) distribution. Gaussian models for
the separation distribution with a peak at a = 4 au and 0.6 =< sigma(log(a/au))
=< 1.0 correctly predict the number of observed binaries, yielding a close
(a<2.6 au) binary frequency of 17-30 per cent and an overall VLMS/BD binary
frequency of 32-45 per cent. We find that the available N-body models of
VLMS/BD formation from dynamically decaying protostellar multiple systems are
excluded at >99 per cent confidence because they predict too few close binary
VLMS/BDs. The large number of close binaries and high overall binary frequency
are also very inconsistent with recent smoothed particle hydrodynamical
modelling and argue against a dynamical origin for VLMS/BDs.
