  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.}
