A linear programming approach to Fuglede’s conjecture in $$\mathbb {Z}_p^3$$

Abstract

We present an approach to Fuglede’s conjecture in $$\mathbb {Z}_p^3$$ Z p 3 using linear programming bounds, obtaining the following partial result: if $$A\subseteq \mathbb {Z}_p^3$$ A ⊆ Z p 3 with $$p^2-p\sqrt{p}+\sqrt{p}<|A|<p^2$$ p 2 - p p + p < | A | < p 2 , then A is not spectral.