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Searching for realistic 4d string models with a Pati–Salam symmetry. Orbifold grand unified theories from heterotic string compactification on a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math>orbifold