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 87Rb atoms above the surface of the magnetic film with one-dimensional and two-dimensional (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 lattices.