The \( n^2 \) computational overhead of PCGs for the OLE/MT correlation has long been a trouble and only recently have we come up with some creative solution (for authenticated triples over \( \mathbb{F}_2 \)).
This is a Crypto 2020 paper that shows how to create such a correlation over \( \mathbb{F}_{2^{\rho}} \) using Ring-LPN. I recall giving talks about this construction in various occacions but the details have been lost now.
Anyway, here is the slides I have prepared for a LATTICE group meeting at Dec. 2021 Slides.