Abstract
A 2-(2n+1,n,λ) design can always be extended to a 3-(2n+2,n+1,λ) design by complementation. If λ is large enough there may be other methods of extension. By constructing non-self-complementary 3-(18,9,7) designs it is shown that there is a 2-(17,8,7) design with 16 extensions. The method generalises to give non-self-complementary 3-(2n+2,n+1,n−1) designs for larger values of n.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D.R. Breach, The 2-(9, 4, 3) and 3-(10,5,3) designs, J. Combinatorial Theory (A) (to appear). (A longer version exists as Research Report CORR 77-11 of the Department of Combinatorics and Optimisation, University of Waterloo, Ontario, Canada.)
P. Dembowski, Finite Geometries (Ergebnisse der Mathematik 44), Springer Verlag, Berlin, 1968.
Marshall Hall, Jr., Combinatorial Theory, Blaisdell, Waltham, Mass., U.S.A. 1967.
J.H. van Lint, H.C.A. van Tilborg, and J.R. Wikeman, Block designs with v=10, k=5, λ=4, J. Combinatorial Theory (A) 23 (1977), 105–115.
D.A. Sprott, Balanced incompletc block designs and tactical configurations, Ann. of Math. Statist., 26 (1955), 752–758.
R.G. Stanton, R.C. Mullin, and J.A. Bate, Isomorphism classes of a set of prime BIBD parameters, Ars Combinatoria 2, (1976), 251–264.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
Breach, D.R. (1979). Some 2-(2n+1,n,n-1) designs with multiple extensions. In: Horadam, A.F., Wallis, W.D. (eds) Combinatorial Mathematics VI. Lecture Notes in Mathematics, vol 748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102682
Download citation
DOI: https://doi.org/10.1007/BFb0102682
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09555-2
Online ISBN: 978-3-540-34857-3
eBook Packages: Springer Book Archive
