Related to Open Problem #1: Knights and Knights

This problem is part of the new Brilliant.org Open Problems Group. The end goal for each open problem is to find a solution, and maybe publish it if it's a nice enough result! Even if we don't make it all the way there, we can have fun exploring unsolved problems and doing real research. This problem is related to an unsolved open problem, which you can read about here.

Place an equal number of white knights and black knights on a square board (of any size) such that

• each white knight is attacking 2 other white knights and 2 black knights;
• each black knight is attacking 2 other black knights and 2 white knights.

What is the side length of the smallest square board on which this is possible?

Note: A chess knight moves in an "L" shape either 1 square vertically and 2 squares horizontally or 2 squares vertically and 1 square horizontally, as indicated by the stars above.