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Also displayed in Fig.~\ref{fig:lumi} are the instantaneous luminosity expected for two linear collider projects, ILC~\cite{cite:ILCTDR} and CLIC~\cite{cite:CLICDR}, as a function of the centre-of-mass energy. It is remarkable that the luminosity expected at TLEP is between one and three orders of magnitude larger that that expected for a linear collider, at all centre-of-mass energies from the Z pole to the $\ttbar$ threshold, where precision measurements are to be made, hence where the accumulated statistics will be a key feature : TLEP is therefore in a unique position to perform these measurements with a meaningful accuracy. The access to the high-energy frontier is discussed in Section~\ref{sec:VHE-LHC} for both the linear and the circular colliders.     Upgrading the luminosity Luminosity upgrades well  beyond the values given above is are  also being investigated -- although it they  cannot be guaranteed today. The goal is to eliminate the sources limiting the beam life time other than the particle-particle interactions themselves. One could then Possibilities include an order-of-magnitude  increasethe luminosoty (for example by reducing the beam size) until the injector capacity is saturated. Since at present the lifetime caused by interactions is estimated to be 16 minutes (1000 seconds), a gain factor of up to 10 in luminosity might in principle be envisaged if injection every 10 seconds of 10\%  of the top-off injection rate and/or  beam is possible. A solution that comes to mind is to eliminate beamstrahlung by means of "charge compensation", charge compensation, as discussed  in which each beam would be accompanied with an additional beam of Ref.~\cite{cite:1305.6498}. The access to  the opposite charge. While this was tried with limited success high-energy frontier is discussed  in Orsay, this technique might be applicable with improved beam controls -- this possibility and the implications Section~\ref{sec:VHE-LHC}  for both  the accelerator design will be investigated as a possible upgrade path of linear and  the machine. circular colliders.