How to calculate airfoil geometry with the maximum lift to drag ratio for a given Reynolds number?
The optimum airfoil is a cambered line of zero thickness. If operated at just the correct angle of attack, it will produce the highest L/D possible. It's cross section is trivial: It has none. However, it will not allow to build a clean wing since it has no space for a spar. It would need to be kept in shape by lots of wire bracing, and then the overall L/D of the resulting aircraft would be horrible.

Next, if the angle of attack is only slightly different from the optimum value, the sharp leading edge will cause early separation on one side, causing the L/D figure to plummet. This airfoil will not be practical for any purpose other than establishing a theoretical optimum figure.

Real airfoils need a blunt nose and some thickness. There are plenty enough airfoils to choose from already. All of them were designed not just for one single design point, but as an overall compromise to cover a wider range of parameters in real-world operation.