  The absolute values of polynomial SLOCC invariants (which always vanish on
separable states) can be seen as measures of entanglement. We study the case of
real 3-qutrit systems and discover a new set of maximally entangled states
(from the point of view of maximizing the hyperdeterminant). We also study the
basic fundamental invariants and find real 3-qutrit states that maximize their
absolute values. It is notable that the Aharonov state is a simultaneous
maximizer for all 3 fundamental invariants. We also study the evaluation of
these invariants on random real 3-qutrit systems and analyze their behavior
using histograms and level-set plots. Finally, we show how to evaluate these
invariants on any 3-qutrit state using basic matrix operations.
