A reactive ion etching (RIE) technique of the surface of GaAs/AlGaAs heterostructures through nitrocellulose mesoscopic regular network precursor was used to produce a novel network-confined 2D system for the study of charge transport. The characteristic dimensions of the fabricated honeycomb GaAs structures (the size of hexagonal cell and the thickness of bonds) were approximately 500 and 50 nm, respectively. The manufactured structures were found to be completely depleted due to RIE damage to the sidewalls. The LED excitation was used in order to increase the conductance of the structures. The dependencies of the photoconductivity on the temperature and on the light intensity in the temperature range 20-120 K were measured. High photoconductivity is believed to be related to inhomogeneity of the investigated structures due to high density of the surface defects.