<p>Traditionally, global navigation satellite system (GNSS) observations in precise point positioning were processed using geometric ionosphere-free (GIF) code and phase linear combinations (LC). With multi-frequency observations of modernized GNSS, the processing of undifferenced and uncombined (UDUC) observations has gained popularity, often attributed to its increased flexibility and generality. Building on the theoretical foundation of UDUC processing, this work derives an equivalent LC-based network processing approach that maintains the full generality of the UDUC approach while offering some practical advantages. The approach makes use of the following types of LCs: (1) geometry-free and ionosphere free (GFIF), (2) geometric ionosphere-free (GIF), and (3) ionospheric geometry-free (IGF). When processing the GFIF LCs, biases and ambiguities can be estimated. The GFIF model enables compact modeling by reducing continuous observation arcs to a single observation and supports (extra-) wide-lane ambiguity resolution. To obtain the ionosphere-free model, i.e., an equivalent reformulation of the UDUC approach where epoch-wise and line of sight specific ionospheric delays are assumed, exactly one GIF LC per line-of-sight and epoch is added to the GFIF LCs. To obtain the geometry-free model, commonly used for ionospheric modeling, exactly one IGF LC is added to the GFIF LCs per line-of-sight and epoch. Adding both the GIF and IGF LCs to the GFIF LCs yields an exact reformulation of the UDUC with no implicit assumptions regarding ionospheric or geometric parameters. Finally, a brief runtime analysis of LC-based models shows case-dependent efficiency gains over UDUC implementations.</p>