On Identifying Codes in the Triangular and Square Grids

It is shown that in the infinite square grid the density of every (r, ≤ 2)-identifying code is at least 1/8 and that there exists a sequence Cᵣ of (r, ≤ 2)-identifying codes such that the density of Cr tends to 1/8 when r → ∞. In the infinite triangular grid a sequence C'ᵣ of (r, ≤ 2)-identifying codes is given such that the density of C'ᵣ tends to 0 when r → ∞.