  The occurrence of planets orbiting ultracool dwarfs is poorly constrained. We
present results from a Guest Observer program on NASA's K2 spacecraft to search
for transiting planets orbiting a sample of 827 ultracool dwarfs. Having found
no transiting planets in our sample, we determined an upper limit on the
occurrence of planets. We simulated planets orbiting our sample for a range of
orbital periods and sizes. For the simulated planets that transit their host,
we injected the transit light curve into the real K2 light curves, then
attempted to recover the injected planets. For a given occurrence rate, we
calculated the probability of seeing no planets, and use the results to place
an upper limit on planet occurrence as a function of planet radius and orbital
period. We find that short period, mini-Neptune- and Jupiter-sized planets are
rare around ultracool dwarfs, consistent with results for early- and mid-type M
dwarf stars. We constrain the occurrence rate $\eta$ for planets between $0.5$
and $10$ R$_{\oplus}$ with orbital periods between 1 and 26.3 days.
