The choice of a 20 gauge shotgun barrel having the smallest bore diameter is correct due to the measurement system used for shotgun gauges. The gauge number inversely correlates to the bore diameter, with a higher gauge number indicating a smaller bore size.
Specifically, a 20 gauge shotgun barrel is designed to fit a lead ball that weighs 1/20th of a pound, translating to a bore diameter of approximately .615 inches. In contrast, a 12 gauge shotgun barrel has a larger bore (about .729 inches), as does the 10 gauge (around .775 inches), while a 16 gauge sits between the 12 and 20 gauges at around .662 inches.
This system means that as the gauge number increases, the diameter decreases, making the 20 gauge the one with the smallest diameter among those listed. The understanding of gauge size is fundamental for hunters and shooters, as it affects the type of ammunition that can be used and ultimately the performance of the shotgun.