On identifying codes in the triangular and square grids

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