# How to prove the existence of the spectral expander with the given parameteres?

I need to prove the existence of the $$(1944, 144, 0.5)$$ spectral expander. I tried to construct it using tensor product of the following graphs: $$(1944, 144, 0.5) = (9^2, 9, 1/3) \otimes (24, 16, 0.5)$$ I already know that expander with parameters $$(9^2, 9, 1/3)$$ exists and corresponds to the affine expander, but I am not sure about $$(24, 16, 0.5)$$ one.

There are also expanders with the following parameters: $$(3, 2, 1/2)$$ — complete graph on 3 vertices and $$(8,8, 0)$$ — complete graph on 8 vertices with the loop in each vertex. So we have the following tensor product: $$(1944, 144, 0.5) = (9^2, 9, 1/3) \otimes (3, 2, 1/2) \otimes (8,8, 0)$$