The concept of Eisenstein integers is applied to place sensors efficiently for a distributed sensor network covering a bounded region on a plane. Eisenstein integer based arrangement is more efficient in the sense that the ratio of the number of sensors required in the sensor network based on Eisenstein integers and that required by the traditional rectangular grid based networks covering the same area is about 1: 1:299. Optimal grid size, sensor coverage density, failure rate as functions of the sensor coverage radius and the sensor failure rate are derived for Eisenstein grid sensor network.
