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Bulletin of the London Mathematical Society Advance Access originally published online on July 17, 2009
Bulletin of the London Mathematical Society 2009 41(5):841-852; doi:10.1112/blms/bdp060
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© 2009 London Mathematical Society

Amalgams of designs and nets

T. P. McDonough

Institute of Mathematics and Physics
Aberystwyth University
Aberystwyth
Ceredigion
SY23 3BZ
United Kingdom
tpd@aber.ac.uk

V. C. Mavron

Institute of Mathematics and Physics
Aberystwyth University
Aberystwyth
Ceredigion
SY23 3BZ
United Kingdom
vcm@aber.ac.uk

H. N. Ward

Department of Mathematics
University of Virginia
Charlottesville, VA 22904
USA

Received 8 December 2008.

We present a procedure for amalgamating a net and a collection of designs into a single design. At first this amalgam is just point-regular, but it acquires additional regularities upon imposing restrictions on the ingredients. At its most regular, the amalgam is quasi-symmetric, and designs with the same parameters as those recently constructed by Bracken, McGuire and Ward appear. Along the way we discuss a class of designs generalising Hadamard designs, and we consider the problem of packing projective planes with disjoint line sets into the same point set.

2000 Mathematics Subject Classification 05B05 (primary), 05B15, 51E14, 94B27 (secondary).

H. N. Ward gratefully thanks Aberystwyth University for its hospitality and the Institute of Mathematics and its Applications for partial support during the preparation of this paper.


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