Maximally supersymmetric AdS4 vacua in N=4 supergravity

We study AdS backgrounds of N = 4 supergravity in four space-time dimensions which preserve all sixteen supercharges. We show that the graviphotons have to form a subgroup of the gauge group that consists of an electric and a magnetic SO(3)(+) x SO(3)(-). Moreover, these N = 4 AdS backgrounds are necessarily isolated points in field space which have no moduli.