New Lower Bounds for Heilbronn Numbers

Abstract

The n-th Heilbronn number, Hn, is the largest value such that n points can be placed in the unit square in such a way that all possible triangles defined by any three of the points have area at least Hn. In this note we establish new bounds for the first Heilbronn numbers. These new values have been found by using a simple implementation of simulated annealing to obtain a first approximation and then optimizing the results by finding the nearest exact local maximum.

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Cite this paper

@article{Comellas2002NewLB, title={New Lower Bounds for Heilbronn Numbers}, author={Francesc Comellas and Jos{\'e} Luis Andres Yebra}, journal={Electr. J. Comb.}, year={2002}, volume={9} }