A tesseral shim coil for shimming the magnetic field of a magnetic resonance system by generating the spherical harmonics of the sine and cosine type of the magnetic field, the tesseral shim coil comprising at least four saddle coils, wherein the sum of the azimuthal span of the at least four saddle coils is less than 360 degrees. First and second sets of shim coils, respectively generating sine and cosine components of the shim fields are combined into a single coil layer, thereby reducing the radial thickness of the shim coil assembly.
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