Upgrade of the Monte Carlo program BHLUMI for Bhabha scattering at low angles to version 4.04

The new version of the Monte Carlo program for small-angle Bhabha scattering BHLUMI with an overall precision of 0.11% is presented, The main improvements are in the matrix element of the main multi-photon sub-generator based on the Yennie-Frautschi-Suura exponentiation, where the missing second-order terms in the leading-logarithmic (LL) approximation are supplemented and the contribution from the Z resonance is improved. In the LUMLOG sub-generator based on the LL approximation, we implement collinear photon emission in the final state and we also add a down-graded third-order LL matrix element, which has exactly the same incomplete third-order LL contribution as the multi-photon BHLUMI. The new LUMLOG is therefore capable of calculating the missing third-order LL part in the cross sections obtained from the main multi-photon event generator, for arbitrary event selection. The first-order event generator OLDBIS remains unchanged.