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Abstract for 
J. B. M. Melissen and P. C. Schuur,
Improved Coverings of a Square with Six and Eight Equal Circles

In a recent article, Tarnai and G\'asp\'ar used computer
simulations to find thin coverings of a square with up to
ten equal circles. We will give improved coverings with six
and eight circles and a new, thin covering with eleven circles,
found by the use of simulated annealing. Furthermore, we
present a combinatorial method for constructing lower bounds
for the optimal covering radius.



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