In [M. Klin, A. Munemusa, M. Muzychuk, P.-H. Zieschang Directed strongly regular graphs obtained from coherent algebras. Linear Algebra and its Applications 337, (2004) 83-109] the flag algebra of a given balanced incomplete block design with parameters (ν, b, r, k, λ) where λ = 1, has been constructed. In this paper, we consider the association scheme which is related to this flag algebra. By ...

We enumerate a list of 594 inequivalent binary (33, 16) doubly-even self-orthogonal codes that have no all-zero coordinates along with their automorphism groups. It is proven that if a (22, 8, 4) Balanced Incomplete Block Design were to exist then the 22 rows of its incident matrix will be contained in at least one of the 594 codes. Without using computers, we eliminate this possibility for 116...

A popular design in large scale' educational assessments is the balanced incomplete block design. The design assumes that the item pool is split into a set of blocks of items that are assigned to assessment booklets. This paper shows how the technique of 0-1 linear programming can be used to calculate a balanced incomplete block design. Several structural as well as practical constraints on thi...

The construction of balanced incomplete block designs is considered using the method of cyclic shifts. An interesting feature of this method is that there is no need to construct the bocks of the actual design to obtain the properties of a design. One can obtain the off-diagonal elements of the concurrence matrix from the sets of shifts with less effort. A catalogue of balanced incomplete block...

Sometimes the number of treatments to be compared is so large that a complete blocks experiment is impractical. This happens, for example, in some agronomic variety trials. A balanced incomplete block (BIB) design can be used in such a situation. In sensory evaluation trials loss of sensitivity can occur when the subjects are not be able to compare more than a few products with any certainty. A...