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An infinite family of non-embeddable quasi-residual designs

✍ Scribed by Kirsten Mackenzie-Fleming; Ken W Smith

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
82 KB
Volume
73
Category
Article
ISSN
0378-3758

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✦ Synopsis

The existence of a (3 d+2 -2; 3 d+1 ; 3 d ); dΒΏ0, Mitchell design together with the existence of a resolvable 2 -(3 d+1 ; 3 d ; (3 d -1)=2) design (i.e. designs with the parmeters of an a ne geometry design) imply the existence of a quasi-residual 2 -(2(3 d+2 -1); 2(3 d+1 ); 3 d+1 ) design D. This paper contains a construction for the designs D; each of the designs D contain a substructure S consisting of 8 blocks of D with speciΓΏed pairwise intersection sizes. A proof is given that the substructure S prevents D from being embedded into a (3 d+3 -2; 3 d+2 ; 3 d+1 ) design. Further, the maximum intersection size of any pair of blocks in D is 3 d+1 , therefore the design D is non-embeddable and not of Bhattacharya type.

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