Abstract
The Fuglede conjecture states that a set is spectral if and only if it tiles by translation. The conjecture was disproved by Tao for dimensions 5 and higher by giving a counterexample in We present a computer program that determines that the Fuglede conjecture holds in
by exhausting the search space. Recently Iosevich, Mayeli and Pakianathan showed that the Fuglede conjecture holds over prime fields when the dimension does not exceed 2. The question for dimension 3 was previously addressed by Aten et al. for p = 3. In this paper we build upon those results by Aten et al. to allow a computer to carry out the lengthy computations.