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Using numerical ray tracing, the paper studies how the average distancemodulus in an inhomogeneous universe differs from its homogeneous counterpart.The averaging is over all directions from a fixed observer not over allpossible observers (cosmic), thus it is more directly applicable to ourobservations. Unlike previous studies, the averaging is exact,non-perturbative, and includes all possible non-linear effects. Theinhomogeneous universes are represented by Sweese-cheese models containingrandom and simple cubic lattices of mass-compensated voids. The Earth observeris in the homogeneous cheese which has an Einstein - de Sitter metric. For thefirst time, the averaging is widened to include the supernovas inside the voidsby assuming the probability for supernova emission from any comoving volume isproportional to the rest mass in it. Despite the well known argument for photonflux conservation, the average distance modulus correction at low redshifts isnot zero due to the peculiar velocities. A formula for the maximum possibleaverage correction as a function of redshift is derived and shown to be inexcellent agreement with the numerical results. The actual average correctioncalculated in random and simple cubic void lattices is severely damped belowthe predicted maximal average. That is traced to cancelations between thecorrections coming from the fronts and backs of different voids at the sameredshift from the observer. The calculated correction at low redshifts allowsone to readily predict the redshift at which the averaged fluctuation in theHubble diagram is below a required precision and suggests a method to extractthe background Hubble constant from low redshift data without the need tocorrect for peculiar velocities.

Average luminosity distance in inhomogeneous universes