Theoretical predictions for neutrino fluxes indicate that km$^{3}$ scale detectors are needed to detect certain astrophysical sources. The three Mediterranean experiments, ANTARES, NEMO and NESTOR are working together on a design study, KM3NeT, for a large deep-sea neutrino telescope. A detector placed in the Mediterranean Sea will survey a large part of the Galactic disc, including the Galactic Centre. It will complement the IceCube telescope currently under construction at the South Pole. Furthermore, the improved optical properties of sea water, compared to Antarctic ice, will allow a better angular resolution and hence better background rejection. The main work presented in this paper is to evaluate different km$^{3}$ scale detector geometries in order to optimize the muon neutrino sensitivity between 1 and 100 TeV. For this purpose, we have developed a detailed simulation based on the {it Mathematica} software - for the muon track production, the light transmission in water, the environmental background and the detector response. To compare different geometries, we have mainly used the effective neutrino area obtained after the full standard reconstruction chain.}
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