## Abstract An (__r__,Ξ»)βdesign with mutually balanced nested subdesigns (for brevity, (__r__,Ξ»)βdesign with MBN) is introduced firstly in this article. It is shown that an __r__,Ξ»βdesign with MBN is equivalent to a balanced array of strength 2 with __s__ symbols. By the use of a nested design and
Mutually balanced nested designs
β Scribed by R. Fuji-Hara; S. Kuriki
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 658 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Fuji-Hara R. and S. Kuriki, Mutually balanced nested designs, Discrete Mathematics 97 (1991) 167-176.
A mutually balanced nested design of strength t is introduced. It is shown that such a nested design is equivalent to a balanced array of strength t. Some recursive constructions are given for a mutually balanced nested design of strength 2. Some constructions are also given for a balanced incomplete array of strength 2 which are based on a mutually balanced nested design.
π SIMILAR VOLUMES
A new series of balanced block designs with nested rows and columns is constructed using the finite Euclidian geometry. Some such designs along the line of Cheng (1986) are also considered. A result on the system of distinct representatives is seen to be helpful in the derivation.
A number of methods of construction of partially balanced inconiplete block designs with nested rows and columns are developed and new balanced incomp1et.e block designs with nested rows and columns are obtained as a by-product.