On the best constant for the Besicovitch covering theorem
Zoltán Füredi, Peter A. Loeb · Proceedings of the American Mathematical Society · 1994
This note shows that in terms of known proofs of the Besicovitch Covering Theorem, the best constant for that theorem is the maximum number of points that can be packed into a closed ball of radius 2 when the distance between pairs of points is at least 1 and one of the points is at the center of the ball. Exponential upper and lower bounds are also established.