On Cyclically Resolvable Cyclic Steiner 2-Designs

In this article, we present a direct construction for cyclically resolvable cyclic Steiner 2-designs which is applicable irrespective of the parity of the block size. As an example, by using Weilʹs theorem on character sums, this construction gives an infinite series of cyclically resolvable cyclic Steiner 2-designs with block size 4 on 4ppoints, wherep=12t+1 is a prime greater than 22581507 andtis odd. With the aid of a computer and some ad hoc constructions, we show that such designs exist also for primes less than 22581507. By applying a known recursive method, we construct other cyclically resolvable cyclic Steiner 2-designs with block size 4 on 4qpoints, whereqis a product of primes of the form 12t+1 andtis odd.