An assessment of the recorded integrated luminosity is presented for data collected with the D0 detector at the Fermilab Tevatron Collider from June 2006 to September 2011 (Run IIb). In addition, a measurement of the effective cross section for inelastic interactions, also referred to as the luminosity constant, is reported. This measurement incorporates new features that lead to a substantial improvement in the precision of the result. A luminosity constant of sigma_{LM} = 48.3pm1.9pm0.6 mb is obtained, where the first uncertainty is due to the accuracy of the inelastic cross section used by both CDF and D0, and the second uncertainty is due to D0 sources. The recorded luminosity for the highest E_T jet trigger is L_rec = 9.2 pm 0.4 fb^{-1}, with a relative uncertainty of 4.3%.
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