Silver nanoparticles (diameters between 2.0 and 6.0 nm) arranged in a 2D hexagonal lattice and embedded in a dielectric matrix are considered in this work. The array resembles somehow the one tailored by Pileni and coworkers, Phys. Rev. B 59, 13350 (1999) to study the electromagnetic coupling between metal nanoparticles and their size effects in the optical absorption coefficient. Non-local and quantum size effects in the nanometric particles are taken into account by means of a size dependent dielectric function which includes level quantization as well as diffuse surface effects.