I am looking for a hypergraphs product of hypergraph H1,H2 that preserves some expansion properties of H1,H2. The expansion property I am looking at is HD-random walk. The product I am looking for is similar to normal hypergraph product, that is similar to a cartesian product, but not very much.

I work in the specific case where H2 is 4-complete hypergraph and H1 is a 3-uniform hypergraph that expands.

I am working on proving that the normal product is OK, but I don't want to reinvent the wheel.

Thanks.