Does anyone have experience with MPRA library construction using degenerate barcodes?

We constructed a library containing ~2,000 oligos, each tagged with a 16N degenerate barcode. After performing NGS at ~100× depth to map oligo–barcode associations, we found that more than 50% of the barcodes had fewer than 3 reads.

I’m wondering if this is a common feature when using degenerate barcodes in MPRA. If so, what is the typical proportion of low-count barcodes (e.g.,