We report on the design, fabrication and characterization of magnetic nanostructures to create a lattice of magnetic traps with sub--micron period for trapping ultracold atoms. These magnetic nanostructures were fabricated by patterning a Co/Pd multilayered magnetic film grown on a silicon substrate using high precision e-beam lithography and reactive ion etching. The Co/Pd film was chosen for its small grain size and high remanent magnetization and coercivity. The fabricated structures are designed to magnetically trap $^{87}$Rb atoms above the surface of the magnetic film with 1D and 2D (triangular and square) lattice geometries and sub-micron period. Such magnetic lattices can be used for quantum tunneling and quantum simulation experiments, including using geometries and periods that may be inaccessible with optical lattice.