We describe the lookup table approach that is used to store pre-calculated absorption data in the radiative transfer model ARTS. The table stores absorption cross sections as a function of frequency, pressure, temperature, and the water vapor volume mixing ratio, where the last dimension is only included for those gas species that require it. The table is used together with an extraction strategy, which uses polynomial interpolation, with recommended interpolation orders between five and seven. We also derived recommended default settings for grid spacings and interpolation orders, and verified that the approach gives very accurate results with these default settings. The tested instrument setups were for AMSU-B, HIRS, and Odin, three well-known satellite remote sensing instruments covering a wide range of frequencies and viewing geometries. Errors introduced by the lookup table were found to be always below a few millikelvin, in terms of the simulated brightness temperature.