For quasi-symmetric 2-designs with intersection numbers 0 and y between 2 and 10, the socle of any flag-transitive point-primitive automorphism group cannot be an exceptional group of Lie type.
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Flag-transitive point-primitive quasi-symmetric $2$-designs and exceptional groups of Lie type
For quasi-symmetric 2-designs with intersection numbers 0 and y between 2 and 10, the socle of any flag-transitive point-primitive automorphism group cannot be an exceptional group of Lie type.