Improved bounds on the size of the smallest representation of relation algebra $32_{65}$

In this paper, we shed new light on the spectrum of relation algebra $32_{65}$. We show that 1024 is in the spectrum, and no number smaller than 26 is in the spectrum. In addition, we derive upper and lower bounds on the smallest member of the spectra of an infinite class of algebras derived from $32_{65}$ via splitting.