We present initial results from a deep neutral hydrogen (HI) survey of the HALOGAS galaxy sample, which includes the spiral galaxies NGC891, NGC925, NGC4414, and NGC4565, performed with the Robert C. Byrd Green Bank Telescope (GBT). The resulting observations cover at least four deg$^2$ around these galaxies with an average 5$sigma$ detection limit of 1.2$times$10$^{18}$ cm$^{-2}$ over a velocity range of 20 km s$^{-1}$ and angular scale of 9.1$$. In addition to detecting the same total flux as the GBT data, the spatial distribution of the GBT and original Westerbork Synthesis Radio Telescope (WSRT) data match well at equal spatial resolutions. The HI mass fraction below HI column densities of 10$^{19}$ cm$^{-2}$ is, on average, 2%. We discuss the possible origins of low column density HI of nearby spiral galaxies. The absence of a considerable amount of newly detected HI by the GBT indicates these galaxies do not have significant extended diffuse HI structures, and suggests future surveys planned with the SKA and its precursors must go textit{at least} as deep as 10$^{17}$ cm$^{-2}$ in column density to significantly increase the probability of detecting HI associated with the cosmic web and/or cold mode accretion.
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