  The fractional quantum Hall effect at $\nu=2+3/8$, which has been
definitively observed, is one of the last fractions for which no viable
explanation has so far been demonstrated. Our detailed study suggests that it
belongs to a new class of of exotic states described by the
Bonderson-Slingerland wave function. Its excitations are non-Abelian anyons
similar to those of the well studied Pfaffian state at 5/2, but its wave
function has a more complex structure. Using the effective edge theory, we make
predictions for various measurable quantities that should enable a confirmation
of the underlying topological order of this state.
