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We present results of a GATE simulation study on the role of different design parameters for the count rate accuracy of a high resolution gamma ray detector used for transmission tomography. The considered gamma ray tomography system is operated with a 137Cs isotopic source and a special detector comprising 320 single elements, made of lutetium yttrium orthosilicate (LYSO) scintillators coupled to avalanche photo diodes (APD). Energy resolution of the detector elements is limited to about 25% which leads to erroneous counting of photons which have been Compton scattered before detection in other parts of the detector and the object. This introduces a linearity error into the tomographic data which leads to artifacts and errors in the reconstructed images. Simulation of the count rate error for the existing configuration shows good agreement with measured detector cross-talk. We investigated different virtual design changes regarding crystal geometry, separation, shielding and arrangement. Results show that further increase in accuracy is possible.