Abstract
An (n+1, 1)-design D is locally extensible at a block B if D can be embedded in an (n+1, 1)-design having a block B * of cardinality n+1 and such that B⊂B *. If D is embeddable in a finite projective plane of order n, then D is called globally extensible. In this paper, we investigate the asymptotic behaviour of locally extensible designs and Euclidean designs. We study the relationship between locally extensible and extensible designs and the uniqueness of such embeddings. It is shown that, for n, l and t sufficiently large, any (n+1, 1)-design which has minimum block length l and which is locally extensible at t of its blocks is globally extensible.
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References
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Mullin, R.C., Vanstone, S.A. Asymptotic properties of locally extensible designs. Geom Dedicata 15, 269–277 (1984). https://doi.org/10.1007/BF00147650
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DOI: https://doi.org/10.1007/BF00147650