New lower bound for 2-identifying code in the square grid

An r-identifying code in a graph G = (V,E) is a subset C ⊆ V such that for each u ∈ V the intersection of C and the ball of radius r centered at u is nonempty and unique. Previously, r-identifying codes have been studied in various grids. In particular, it has been shown that there exists a 2-identifying code in the square grid with density 5/29 ≈ 0.172 and that there are no 2-identifying codes with density smaller than 3/20 = 0.15. Recently, the lower bound has been improved to 6/37 ≈ 0.162 by Martin and Stanton (2010). In this paper, we further improve the lower bound by showing that there are no 2-identifying codes in the square grid with density smaller than 6/35 ≈ 0.171.