  We present a generalized criterion for maximally entangled nine-qubit states,
whose minimum averaged subsystem purity should be equal to 1/14. In this note,
we prove that absolutely maximally entangled state for nine qubits does not
exist. Further, we construct a new genuine nine-qubit maximally entangled
states of 110,15 and 1 balanced purities equal to 1/16, , 1/8 and and 1/4,
respectively. We found that, the marginal density matrices for subsystems of
1,2,3- qubits all completely mixed in these states, therefore, maximally
entangled nine-qubit state is a 3-uniform state.
