## Abstract The necessary conditions for the existence of a superβsimple resolvable balanced incomplete block design on __v__ points with __k__β=β4 and Ξ»β=β3, are that __v__ββ₯β8 and __v__ββ‘β0βmodβ4. These conditions are shown to be sufficient except for __v__β=β12. Β© 2003 Wiley Periodicals, Inc.
Super-simple resolvable balanced incomplete block designs with block size 4 and index 2
β Scribed by Xiande Zhang; Gennian Ge
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 166 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
The necessary conditions for the existence of a superβsimple resolvable balanced incomplete block design on v points with block size k = 4 and index Ξ» = 2, are that vββ₯β16 and $v \equiv 4; (\bmod; {12})$. These conditions are shown to be sufficient. Β© 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341β356, 2007
π SIMILAR VOLUMES
## 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
## 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
We consider direct constructions due to R. J. R. Abel and
## 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