2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 129132
author:  Veerle Fack, Svetlana Topalova and Joost Winne 

title:  On the enumeration of uniquely reducible double designs 
keywords:  double design, projective plane, enumeration 
abstract: 
A double 2(
v
,
k
,
2λ
) design is a design which is reducible into two 2(
v
,
k
,
λ
) designs. It is called uniquely reducible if it has,
up to equivalence, only one reduction. We present
properties of uniquely reducible double designs which show
that their total number can be determined if only the
designs with nontrivial automorphisms are classified with
respect to their automorphism group. As an application,
after proving that a reducible 2(21,5,2) design is
uniquely reducible, we establish that the number of all
reducible 2(21,5,2) designs is 1 746 461 307.

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reference:  Veerle Fack and Svetlana Topalova and Joost Winne (2005), On the enumeration of uniquely reducible double designs, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 129132 
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