Vandermonde sets and super-Vandermonde sets

Given a set T ⊆ GF(q), |T | = t, wT is defined as the smallest positive integer k for which ∑ y∈T y k 6= 0. It can be shown that wT ≤ t always and wT ≤ t − 1 if the characteristic p divides t. T is called a Vandermonde set if wT ≥ t−1 and a super-Vandermonde set if wT = t. This (extremal) algebraic property is interesting for its own right, but the original motivation comes from finite geometries. In this paper we classify small and large super-Vandermonde sets.