We define an ordering over the set G(n, ϱ, τ) of all 0-1-vectors of dimensionnwith at least ϱ and at most τ positive components. A rule is given to calculate the followerx'∈ G (n, ϱ, τ) of an elementx∈ G (n, ϱ, τ) according to this ordering. The theorems 2-7 contain properties of the ordered set G (n, ϱ, τ) and construction methods for special elements of this set.