A necessary condition is given for the existence of some Generalised Bhaskar Rao designs (GBRDs) with odd block size over cyclic groups of even order. Some constructions are given for GBRDs over cyclic groups of even order with block size 3 and with block size 4. AMS Subject Classification: 05B99 J( ey words and phrases: Balanced Incomplete Block Designs; Generalised Bhaskar Rao Designs

Group divisible designs are the most important class of partially balanced incomplete block (PBIB) designs. A list of new group divisible designs with r, k ⩽ 10 is provided.

Let B(k, λ) be the spectrum of integers n such that there exists a Sλ(2, k, n), a balanced incomplete block design of order n, block size k and index λ. Lindner and Rosa [6] introduced the definition of a Sλ(2, 4, n) having a metamorphosis into a Sλ(2, 3, n) and proved that the necessary condition n ∈ B(3, λ) ∩B(4, λ) is also sufficient. The aim of this paper is to present two different general...

In an effort to detect hidden biases due to failure to control for an unobserved covariate, some observational or nonrandomized studies include two control groups selected to systematically vary the unobserved covariate. Comparisons of the treated group and two control groups must, of course, control for imbalances in observed covariates. Using the three groups, we form pairs optimally matched ...

All the symmetric balanced incomplete block (SBIB) designs have been characterized and a new generalized expression on parameters of SBIB designs has been obtained. The parameter b has been formulated in a different way which is denoted by bi, i = 1, 2, 3, associating with the types of the SBIB design Di. The parameters of all the designs obtained through this representation have been tabulated...

A frequently encountered problem in peer review systems is to facilitate pairwise comparisons of a given set of proposals by as few as referees as possible. In [8], it was shown that, if each referee is assigned to review k proposals then n(n-1)/k(k-1) referees are necessary and n(2n-k)/k referees are sufficient to cover all n(n-1)/2 pairs of n proposals. While the upper bound remains withi...