On identification in the triangular grid

A subset C of vertices in a connected graph G=(V,E) is called (r,⩽l)-identifying if for all subsets L⊆V of size at most l, the sets I(L), consisting of all the codewords which are within graphic distance r from at least one element in L, are different. It is proved that the minimum possible density of a (1,⩽2)-identifying code in the triangular grid is 9/16.