To have a concrete example in mind: 3-qubit Toffoli gate can be decomposed into 6 $CNOT$s as shown here

[![enter image description here](https://i.stack.imgur.com/hjuXn.png)](https://i.stack.imgur.com/hjuXn.png)

I believe this is the most economic decomposition in terms of the number of $CNOT$s used. My questions are:

1. Is it proven that it is not possible to do better than with 6 $CNOT$s?
2. Could the decomposition be improved if ancilla qubits are allowed?

OK, and a 3-qubit Toffoli is really just an example, I would be interested in any results along these lines concerning some standard multi-qubits gates, say $n-$Toffoli, other multi-controlled gates etc.