New constructions for SBIBDs with parameters (v, k, A) = (45, 12, 3), (36, 15, 6), and (40, 13, 4) are given in this note. (~) 2000 Elsevier Science Ltd. All rights reserved.
N-way balanced incomplete block designs
β Scribed by Ching-Shui Cheng
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 141 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0378-3758
No coin nor oath required. For personal study only.
β¦ Synopsis
We construct a family of n-dimensional designs with the property that all the two-dimensional margins are balanced incomplete block designs. Combinatorial and statistical properties of these designs as balanced main-e ect plans are discussed. It is shown that there are nonisomorphic designs with di erent statistical e ciencies. Designs which are more e cient are identiΓΏed.
π SIMILAR VOLUMES
The concept of generalized partially balanced incomplete block (PBIB) design is introduced. Generalized PBIB designs are shown to be useful for the construction of equireplicate balanced block designs, pairwise balanced designs and BIB designs.
## Abstract The necessary conditions for the existence of a balanced incomplete block design on Ο ββ₯β__k__ points, with index Ξ» and block size __k__, are that: For __k__β=β8, these conditions are known to be sufficient when Ξ»β=β1, with 38 possible exceptions, the largest of which is Ο β=β3,753. For