Chebyshev systems of minimal degree

Let $F = \{ {f_i } \}_{i = 0}^n $ be a set of continuous functions on $[a,b]$, and let $F^ * = \{ {f_i f_j } \}_{i,j = 0}^n $. We determine conditions on $F$ which are necessary and sufficient for the set $F^ * $ to be a Chebyshev system on $[a,b]$ consisting of exactly $2n + 1$ distinct functions. The results have applications in the field of experimental design.