Study of theoretical luminosity precision for electron colliders at higher energies

We present an estimation of the theoretical precision of low angle Bhabha scattering at the proposed future ILC collider at 500 GeV. The analysis is an extension of the previous analysis done for the FCCee collider at $\sqrt{s}$=M${}_Z$. As the state-of-the-art and the reference point we use the BHLUMI Monte Carlo event generator. Based on the current precision status of BHLUMI for LEP analysis, we estimate how various error components evolve from the LEP to ILC setups. The conclusion of our work is that for the ILC the precision of the current version of BHLUMI 4.04 deteriorates to 0.5%, by more than an order of magnitude w.r.t. the present precision for LEP. With the expected future improvements, the precision of BHLUMI can change to 0.016%, nearly as good as for the FCCee at the M${}_Z$ setup (0.01%). Based on the developed methodology we present also results for ILC${}_{1000}$, FCCee${}_{350}$ and CLIC${}_{3000}$ setups.