Approaching the Soundness Barrier: A Near Optimal Analysis of the Cube versus Cube Test

Dor Minzer, Kai Zheng

The Cube versus Cube test is a variant of the well-known Plane versus Plane test of Raz and Safra, in which to each $3$-dimensional affine subspace $C$ of ${\mathbb{F}}_q^n$, a polyn…