## 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
New Designs with Block Size 7
β Scribed by Zvonimir Janko; Vladimir D Tonchev
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 148 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
β¦ Synopsis
An imprimitive permutation group of order 4200 is used for the construction of a 2-(175, 7, 1) design. The design yields also a group divisible design 7&GDD and a generalized Bhaskar Rao design GBRD(25, 100, 28, 7, 7; Z 7 ).
π SIMILAR VOLUMES
For k ! 3 the existence problem forvY 7Y k BIBDs has been completely solved, except when v 253. In this paper, 3 new direct vY 7Y k BIBD constructions are given for vY k 259Y 1Y 106Y 2Y and 253Y 2. Some features of the known 175Y 7Y 1 BIBD are also discussed. Finally, a few vY 7Y 1 BIBDs are obtaine
## Abstract In this paper, we determine the number of the orbits of 7βsubsets of $X= {\rm GF}(2^n)\cup\{\infty\}$ with a fixed orbit length under the action of PSL(2, 2^__n__^). As a consequence, we determine the distribution of Ξ» for which there exists a simple 3β(2^__n__^β+β1, 7, Ξ») design with P
## Abstract Let __v,k__, and __n__ be positive integers. An incomplete perfect Mendelsohn design, denoted by __k__βIPMD__(v,n)__, is a triple (__X, Y__, πΉ) where __X__ is a __v__βset (of points), __Y__ is an __n__βsubset of __X__, and πΉ is a collection of cyclically ordered __k__βsubsets of __X__ (
## Abstract Splitting balanced incomplete block designs were first formulated by Ogata, Kurosawa, Stinson, and Saido recently in the investigation of authentication codes. This article investigates the existence of splitting balanced incomplete block designs, i.e., (__v__, 3__k__, Ξ»)βsplitting BIBD