A simple fabrication method of honeycomb-shape networks with characteristic dimensions (the size of hexagonal cell and the thickness of bonds) approximately 500 and 50 nm, respectively, on a semiconductor surface was used in order to decrease dimension of 2-D gas with electron density of 1x10(12) cm(-2) in the initial GaAs/AlGaAs delta-doped heterostructures. Magnetoresistance (MR) in pulsed magnetic fields up to 12 T and the temperature dependencies of resistance in the low-dimensional regular GaAs-networks were measured in the temperature range 2.2-100 K. In low magnetic fields MR was negative and related to quantum interference in the variable range hopping transport along neighboring alternative paths. At higher temperatures with the hopping length decreasing the negative MR due to quantum interference becomes negligibly small. The ordinary behavior of the MR in variable range hopping regime (decreasing of the positive MR with the increasing of the temperature as a result of the electronic wave functions shrinkage by the magnetic field) was observed.