Steiner quadruple systems having a prescribed number of quadruples in common
β Scribed by Giovanni Lo Faro
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 378 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
## Abstract A Steiner quadruple system of order 2^__n__^ is __SemiβBoolean__ (SBQS(2^__n__^) in short) if all its derived triple systems are isomorphic to the pointβline design associated with the projective geometry __PG__(__n__β1, 2). We prove by means of explicit constructions that for any __n__
## Abstract Assmus [1] gave a description of the binary code spanned by the blocks of a Steiner triple or quadruple system according to the 2βrank of the incidence matrix. Using this description, the author [13] found a formula for the total number of distinct Steiner triple systems on 2^__n__^β1 p
We consider t-designs with \*=1 (generalized Steiner systems) for which the block size is not necessarily constant. An inequality for the number of blocks is derived. For t=2, this inequality is the well known De Bruijn Erdo s inequality. For t>2 it has the same order of magnitude as the Wilson Petr