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Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for non-trivial $n$.

I have adopted this metric in my research. One of the reviewers of my paper insists that there must be a closed-form solution for the lower-bound of this second moment (i.e. the optimal packing) for general $n$, because the problem "seems simple".

I do not believe that this is so. Can you please confirm (or prove me wrong)? A reference confirming the unsolved status of this problem would be most welcome.

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1 Answer 1

Slightly old, but the only proved (circle in circle) optimal packings are for $n \leq 20$ http://hydra.nat.uni-magdeburg.de/packing/cci/

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