The goal of this paper is to present a new relationship between the quality criteria for geodetic networks. The quality criteria described here are fourfold: positional uncertainty of network points, considering both bias and precision (at a given confidence level); the maximum allowable number of undetected outliers; the level of reliability and its homogeneity for the observations; and the minimum power of the data snooping test procedure for multiple alternative hypotheses. The highlights consist of the use of advanced concepts, such as reliability measures for multiple outliers and the power of the test for multiple alternative hypotheses (instead of the single outlier and/or the single alternative hypothesis case); and a sequential computational procedure, wherein the quality criteria are mathematically related, instead of being treated as separate criteria. Its practical application is demonstrated numerically in the design of a real horizontal network. A satisfactory performance was achieved by means of simulations. Furthermore, Monte Carlo experiments were conducted to verify the power of the test and the positional uncertainty following the approach proposed. Results provide empirical evidence that the quality criteria present realistic outputs.