Beyond simplicial complexes for double samplers

Identify and construct non-simplicial objects that can serve as double samplers with overhead better than quasipolynomial, thereby surpassing the limitations shown for simplicial complexes.

Background

The paper proves that standard simplicial complexes used to build double samplers cannot achieve better than quasipolynomial overhead and nearly matches this bound. To improve beyond this barrier, one may need to go outside the simplicial framework.

Double samplers are central in applications to list-decodable codes and data structures; improved overhead would directly enhance rates and efficiency.