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# Asymptotic Behavior of Optimal Circle Packings in a Square

Published:1999-09-01
Printed: Sep 1999
• Kari J. Nurmela
• Patric R. J. Östergård
• Rainer aus dem Spring
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## Abstract

A lower bound on the number of points that can be placed in a square of side $\sigma$ such that no two points are within unit distance from each other is proven. The result is constructive, and the series of packings obtained contains many conjecturally optimal packings.
 Keywords: asymptotic bound, circle packing
 MSC Classifications: 52C15 - Packing and covering in $2$ dimensions [See also 05B40, 11H31]