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The Next European Dipole (NED) activity supported by the European Union aims at the development of a high-performance Nb3Sn conductor (Jc = 1500 A/mm2 @ 15 T, 4.2 K) in collaboration with European industry and at the design of a high- field dipole magnet making use of this conductor. In the framework of the NED collaboration which coordinates the activity of several institutes, CERN has contributed to the electromagnetic design study of a cos - thetas, layer-type superconducting dipole with an 88 mm aperture that is able to reach 15 T at 4.2 K. Part of the optimization process was dedicated to the reduction of the multipole coefficients so as to improve field quality while keeping an efficient peak-field to main-field ratio. In this paper, we present the optimization of the coil cross-section and of the shape of the iron yoke to reduce saturation-induced field errors during ramp. The effects of persistent magnetization currents are also estimated and different methods to compensate persistent-current-induced field distortions are presented.