The existence of simple S3(3, 4, v)

Abstract It has been known for some time that an S 3 (3, 4, υ) exists iff υ is even. The constructions which prove this result, in general, give designs having repeated blocks. Recently, it was shown that a simple S 3 (3, 4, υ) exists if υ is even and υ ≢ 4 (mod 12). In this paper we give an elementary proof of the existence of simple S 3 (3, 4, υ) s for all even υ, υ > 4.