I am using QField on an Android tablet, I would like to know if I could use a web mapping service like open street map as a base map. Without having the actual file stored on the tablet?
QField supports many map sources as backend, file, database and web-based like WMS and WMTS.
Among these supported formats is the Tile Server (XYZ) provider. This can be used to integrate maps like OSM and others. See this answer for how to integrate this into your QGIS project.
Do you know QuickMapsServices plugin fort QGIS? This plugin provide more than 500 base maps (OpenStreetMap too).
The QMS service also integrated with NextGIS Mobile (a QField alternative). See documentation about how to add base map: http://docs.nextgis.com/docs_ngmobile/source/load_geodata.html#creating-raster-layer-from-external-geoservice