The existence of modiied group divisible designs with block size four is settled with a handful of possible exceptions.

The pay-per-view (PPV) TV industry is growing fast. The purpose of PPV is to earn revenue from subscribers. However, due to illegal accessing issues, the providers come up with protection method. The protection process from piracy is studied in this paper. The proposed method is based on frequency domain. The simulation results confirm that the proposed method is efficient for scrambling conten...

Each parallel class of a uniformly resolvable design (URD) contains blocks of only one block size k (denoted k-pc). The number of k-pcs is denoted rk. The necessary conditions for URDs with v points, index one, blocks of size 3 and 5, and r3, r5 > 0, are v ≡ 15 (mod 30). If rk > 1, then v ≥ k2, and r3 = (v−1−4 · r5)/2. For r5 = 1 these URDs are known as group divisible designs. We prove that th...

We establish that the necessary conditions for the existence of Bhaskar Rao designs of block size ve are : i). (v 1) 0 (mod 4) ii). v(v 1) 0 (mod 40) iii). 2j. We show these conditions are suucient: for = 4 if v > 215, with 10 smaller possible exceptions and one deenite exception at v = 5; for = 10 if v > 445, with 11 smaller possible exceptions, and one deenite exception at v = 5; and for = 20...

Balanced sampling plans excluding contiguous units (or BSEC) were first introduced by Hedayat, Rao and Stufken in 1988. In this paper, we discuss these designs having cyclic automorphisms. We use Langford sequence to construct all admissible cyclic BSEC (or CBSEC) of block size 3. As consequent we obtain that the existence spectrum of a CBSEC(v, 3, ) are either v ∈ {1, 3}, or v 9 and (v − 3) ≡ ...

The cardinality of the minimal pairwise balanced designs on v elements with largest block size k is denoted by g(k)(v). It is known that 31 ≤ g(4)(18) ≤ 33. In this paper we show that g(4)(18) 6= 31.

We find the graphs of valency at most 7 with the property that any two nonadjacent vertices have either 0 or 2 common neighbours. In particular, we find all semibiplanes of block size at most 7.

By an FGDRP(3, g), we mean a uniform frame (X,G,A) of block size 3, index 2 and type g, where the blocks of A can be arranged into a gu/3× gu array. This array has the properties: (1) the main diagonal consists of u empty subarrays of sizes g/3×g; (2) the blocks in each column form a partial parallel class partitioning X \G for some G ∈ G, while the blocks in each row contain every element of X...

Introduction

Beautifully Ordered Balanced Incomplete Block Designs, BOBIBD(v, k, λ, k1, λ1), are defined and the proof is given to show that necessary conditions are sufficient for the existence of BOBIBD with block size k=3 and k1=2 and for k=4 and k1=2 except possibly for eleven exceptions. Existence of BOBIBDs with block size k=4 and k1=3 is demonstrated for all but one infinite family and the non-existe...