Factorizations of symmetric designs
โ Scribed by D de Caen; D.A Gregory
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 753 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
An embedding theorem for certain quasi-residual designs is proved and is used to construct a series of symmetric designs with v = (1 + 16 + ... + 16")9 + 16 "+~, k =(1 + 16 + ... + 16m)9, and 2 = (1 + 16 + ... + 16m-~)9 + 16".3, for a non-negative integer m.
For q, an odd prime power, we construct symmetric 2q 2 2q 1Y q 2 Y 1 2 qq ร 1 designs having an automorphism group of order q that ยฎxes 2q 1 points. The construction indicates that for each q the number of such designs that are pairwise non-isomorphic is very large.
In this paper, using the construction method of [3], we show that if q > 2 is a prime power such that there exists an afhne plane of order q -1, then there exists a strongly divisible 2 -((q -l)(qh -l), qh-'(q -l), qh-') design for every h 2 2. We show that these quasi-residual designs are embeddabl