As I have remarked many times (often here), these very nice beads are post-Roman Period, from the Byzantine or Early Islamic Periods—which we can tell by the cane patterns that include external stripes.

I have seen three or four of these necklaces, including in the Liese and Lindstrom Collections. They sometimes include reworked elements that I surmise are probably recycled from broken beads (or other sorts of pieces).

JDA.