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∈Tyk≠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.