Sphere packings give an explicit bound for the Besicovitch Covering Theorem

@article{Sullivan1994SpherePG,
  title={Sphere packings give an explicit bound for the Besicovitch Covering Theorem},
  author={John M. Sullivan},
  journal={The Journal of Geometric Analysis},
  year={1994},
  volume={4},
  pages={219-231}
}
We show that the number of disjointed families needed in the Besicovitch Covering Theorem equals the number of unit spheres that can be packed into a ball of radius five, with one at the center, and get estimates on this number. 

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