Reconfigurable intelligent surfaces (RISs) allow controlling the propagation environment in wireless networks through reconfigurable elements. Recently, beyond diagonal RISs (BD-RISs) have been proposed as novel RIS architectures whose scattering matrix is not limited to being diagonal. However, BDRISs have been studied assuming continuous-value scattering matrices, which are hard to implement in practice. In this paper, we address this problem by proposing two solutions to realize discrete-value group and fully connected RISs. First, we propose scalar-discrete RISs, in which each entry of the RIS impedance matrix is independently discretized. Second, we propose vector-discrete RISs, where the entries in each group of the RIS impedance matrix are jointly discretized. In both solutions, the codebook is designed offline such as to minimize the distortion caused in the RIS impedance matrix by the discretization operation. Numerical results show that vector-discrete RISs achieve higher performance than scalar discrete RISs at the cost of increased optimization complexity. Furthermore, fewer resolution bits per impedance are necessary to achieve the performance upper bound as the group size of the group connected architecture increases. In particular, only a single resolution bit is sufficient in fully connected RISs to approximately achieve the performance upper bound.

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