I would be negatively (which in my own personal worldview of being a pessimist means not really) surprised if someone had not yet developed an algorithm to determine the answer to that very exact question. It would be nice to see a big multidimensional matrix of airspeed/fuel consumption/propeller design/engine type/fuel, but then again, I'm firmly a jet/rocket guy myself - why waste any effort on open air exposed whirligigs that really have to struggle to even get to Mach 1?
Theodorsen pretty much solved propellers. Unfortunately it came right on the tail end of piston engine aircraft. I'd guess that the few companies who really need high performance props with big turboprops have done what you've asked, but they aren't sharing their methods.
This looks more like a PR stunt than anything else to me. Its hard to see how 11 blades would be worth it, even if the prop diameter is really constrained.