| Abstract: | We exhibit cyclic (Kv, Ck)‐designs with v > k, v ≡ k (mod 2k), for k an odd prime power but not a prime, and for k = 15. Such values were the only ones not to be analyzed yet, under the hypothesis v ≡ k (mod 2k). Our construction avails of Rosa sequences and approximates the Hamiltonian case (v = k), which is known to admit no cyclic design with the same values of k. As a particular consequence, we settle the existence question for cyclic (Kv, Ck)‐designs with k a prime power. © 2004 Wiley Periodicals, Inc. J Combin Designs 12: 299–310, 2004. |
