The ornamental design for a barrel mount with opticalsight base mount, as shown and described.
FIG. 1 is a perspective view of a barrel mount with an optical sight base mount showing my new design, which is a shotgun barrel mount.
FIG. 2 is a front view thereof.
FIG. 3 is a rear view thereof.
FIG. 4 is a right view thereof.
FIG. 5 is a left view thereof.
FIG. 6 is a top view thereof.
FIG. 7 is a bottom view thereof.
FIG. 8 is a perspective view of the barrel mount with the optical sight base mount, illustrating a microdot being coupled on the optical sight base mount and two side rail mounts being coupled at the barrel mount; and,
FIG. 9 is a perspective view of the barrel mount with the optical sight base mount, illustrating two side rail mounts being coupled at the barrel mount and one side rail mount being coupled on the optical sight base mount.
The broken line portion of the figure drawings is included to show unclaimed subject matter only and forms no part of the claimed design.