measure theory - Example of a Lebesgue measurable set that can't be constructed from Borel sets and projections?

The Borel sigma algebra on $\mathbb{R}^n$ is obtained by starting with open sets and repeatedly applying the operations of complement, countable union, countable intersection. Now Henri Lebesgue famously made the mistake of thinking that the projection of a Borel set is always a Borel set. In reality, the projection of a Borel set need not be a Borel set, although it is still Lebesgue measurable. So that is a way of constructing a Lebesgue measurable set that is not a Borel set.

But my question is, what is an example of a Lebesgue measurable set that cannot be constructed in this way? That is, what is a Lebesgue measurable set that cannot be constructed by starting with open sets in $\mathbb{R}^n$ and repeatedly applying the operations of complement, countable union, countable intersection, and projection?