On 2-designs

AbstractDenote by Mv the set of integers b for which there exists a 2-design (linear space) with v points and b lines. Mv is determined as accurately as possible. On one hand, it is shown for v > v0 that Mv contains the interval [v + p + 1, v + p + q − 1]. On the other hand for v of the form p2 + p + 1 it is shown that the interval [v + 1, v + p − 1] is disjoint from Mv; and if v > v0 and p is of the form q2 + q, then an additional interval [v + p + 1, v + p + q − 1] is disjoint from Mv