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In this paper, we give a method to construct non-symmetric associationschemes of class $3$ from non-symmetric association schemes of class $2$. Thisconstruction is a non-symmetric analogue of the construction of Taylor graphsas an antipodal double cover of a complete graph. We also mention how ourconstruction interact with doubling introduced by Pasechnik.

Extended double covers of non-symmetric association schemes of class $2$