Neighbor Balanced Block Designs for Two Factors

An Algorithm to Generate Neighbor Balanced Binary Block Designs

Ahmed and Akhtar (2007) developed some algorithms to generate neighbor balanced designs. Here, a new algorithm is developed to generate circular neighbor balanced binary block designs for v = 2k in 2(v-1) blocks when blocks are well separated. A catalogue of circular neighbor balanced binary block designs for v up to 50 is presented.

Splitting balanced incomplete block designs

Balanced Arrays of Strength Two from Block Designs

Some constructions of balanced arrays of strength two are provided by use of rectangular designs, group divisible designs, and nested balanced incomplete block designs. Some series of such arrays are also presented as well as orthogonal arrays, with illustrations. # 2002 Wiley Periodicals, Inc. J Combin Designs 10: 303–312, 2002; Published online in Wiley InterScience (www.interscience.wiley.co...

Optimality of neighbor-balanced designs for total effects

The purpose of this paper is to study optimality of circular neighborbalanced block designs when neighbor effects are present in the model. In the literature many optimality results are established for direct effects and neighbor effects separately, but few for total effects, that is, the sum of direct effect of treatment and relevant neighbor effects. We show that circular neighbor-balanced de...

Remarks on Balanced Incomplete Block Designs

Proof. Assume the hypothesis and the falsity of either conclusion. Construct matrix A of 2x + 2 rows and 4x+4 columns, with entries + 1 and — 1. The first column contains exclusively +1, and the second column — 1. Set up one-to-one correspondences between rows of A and elements of D ; between columns other than the first two of A and blocks of D. Enter +1 if the element is contained in the bloc...