An upper bound of $\frac 2 5$.
See [Minimal overlapping under translation.](https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-62/issue-6)
by *T. S. Motzkin*, *K. E. Ralston* and *J. L. Selfridge*,
in "The summer meeting in Seattle" by *V. L. Klee Jr.*, Bull. Amer. Math. Soc.62, p. 558, 1956
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