Some 3-designs and a 4-design

AbstractIn this paper we construct an infinite class of 3-designs and one 4-design by means of a generalization of the method of [1]. For the 3-designs of [2] and [3] k = 4. For those of [4] v = q + 1 where q is a prime power. For our 3-designs v − 1 is any odd divisor of (k2) which is greater than 2k. Such designs will exist for every k not of the form 2r or 2r + 1. For none of these designs is v − 1 a prime power. The 4-design constructed has parameters (v, k, λ) = (18, 5, 4)