  We compute all master integrals for massless three-loop four-particle
scattering amplitudes required for processes like di-jet or di-photon
production at the LHC. We present our result in terms of a Laurent expansion of
the integrals in the dimensional regulator up to 8$^{\text{th}}$ power, with
coefficients expressed in terms of harmonic polylogarithms. As a basis of
master integrals we choose integrals with integrands that only have logarithmic
poles - called $d$log forms. This choice greatly facilitates the subsequent
computation via the method of differential equations. We detail how this basis
is obtained via an improved algorithm originally developed by one of the
authors. We provide a public implementation of this algorithm. We explain how
the algorithm is naturally applied in the context of unitarity. In addition, we
classify our $d$log forms according to their soft and collinear properties.
