B) is said to have the Size Four property if the blocks in B can be partitioned into two isomorphic sets. In this paper we construct block with four with the property, thus the exception of 6 A. Rosa [4]).

The minimum number of blocks having maximum size precisely four that are required to cover, exactly λ times, all pairs of elements from a set of cardinality v is denoted by g λ (v) (or g (4)(v) when λ = 1). All values of g (4) λ (v) are known except for λ = 1 and v = 17 or 18. It is known that 30 ≤ g(4)(17) ≤ 31 and 32 ≤ g(4)(18) ≤ 33. In this paper we show that g(4)(17) 6= 30 and g(4)(18) 6= 3...

The design (15,21,7,5,2) is the only BIBD of block size 5 that does not exist. If it did exist, it would provide an exact bicovering, in 21 blocks of size 5, of the pairs from 15 points. However, we show that 22 quintuples are sufficient to provide a bicover of the pairs from 15 points; thus there are only 10 repetitions required in the bicovering.

The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: λ(v − 1) ≡ 0 mod (k − 1) λv(v − 1) ≡ 0 mod k(k − 1) Earlier work has studied k = 9 with λ ∈ {1, 2, 3, 4, 6, 8, 9, 12}. In this article we show that the necessary conditions are sufficient for λ = 9 and every other λ not previously studied.

The purpose of this paper is to present a large number of highly A-efficient incomplete block designs for making comparisons among a set of test treatments and a control treatment. These designs are BTIB designs. A simple method of construction of BTIB designs, based on BIB designs is proposed. The advantage of this method is that one can use the vast literature on BIB designs to obtain a large...

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...