This thesis investigates room acoustic diffusers based on number sequences, exploring their shortcomings and presents improvements. Standard Phase Grating Diffusers display frequencies where they act like flat plates and fail to diffuse. To overcome this, two new sequences (Luke and power residue) are introduced. The diffusers based on these sequences display extended frequency range compared to standard ones such as Quadratic Residue and Primitive Root Diffusers. Their performance is studied using Boundary Element Modelling which shows that they can avoid flat plate phenomena in the audible frequency range. Furthermore, it is shown that by taking advantage of their inner symmetries Quadratic Residue and Primitive Root Diffusers can be created from smaller components thus allowing for the flat plat effect to be mitigated. Next, Absorption Grating Diffusers are investigated. They consist of ideally absorbing and reflecting elements. For their implementation heavily damped Helmholtz Resonators are investigated showing that they give an approximation of the required distribution of admittance on the surface. Then the performance of ideal Absorption Grating Diffusers is investigated using Boundary Element Modelling. Even with idealised completely absorbing elements, the performance of the diffuser is shown not to achieve substantial diffusion. This arises because edge diffraction from the reflecting elements weakens at high frequencies. At frequencies where smaller elements are creating substantial scattering, larger elements are producing specular reflections. Furthermore, due to the lack of cancellation, the specular reflected lobe is insufficiently attenuated, because it can only be changed through absorption. Improvements to the original design are suggested. By changing reflective elements to reactive ones, scattering can be extended to higher frequencies. This allows for a range of frequencies were more reflecting elements display substantial dispersion. Also, implementing the absorbing elements using porous material in a shallow well allows some reflection, resulting in cancellation in the specular reflection lobe due to interference. Measurements of the scattered pressure distribution of absorption grating surfaces are carried out and then compared to Boundary Element Modelling simulations using surface admittance data measured in an impedance tube. The agreement between measurement and simulation is excellent proving the accuracy of this simulation method for these applications. The results show that the samples tested perform as two level Phase Grating Diffusers, with some energy loss, while their diffusion characteristics are shifted to lower frequencies. This arises because of the lower speed of sound in the porous medium. This implementation is shown to absorb 50% of the incident sound while the rest is scattered uniformly but only over a limited bandwidth.