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On balanced incomplete-block designs with repeated blocks. (English) Zbl 1127.05009

In this highly informative paper, balanced incomplete block designs (BIBDs or \(2\)-designs) mainly with repeated blocks are studied. Along with this, results on several other types of designs such as \(t\)-designs, \(t\)-wise balanced designs and designs with different block sizes are also obtained. Initial results in this direction date back to R. C. Bose, H. B. Mann and van Lint and Ryser.
The paper under review discusses these results and also obtains many new results. A large number of assertions in this paper use the package GAP. The paper is thus highly suitable for researchers in the major area of constructive design theory; it gives a wealth of information (including automorphism groups) on several parameters of designs.

MSC:

05B05 Combinatorial aspects of block designs
05B25 Combinatorial aspects of finite geometries
05B30 Other designs, configurations
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References:

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