Geometriae Dedicata
1572-9168
Springer Nature
0046-5755
R. C.
Mullin
Department of Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
St. Jerome's College, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
Department of Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
St. Jerome's College, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
articles
finite projective plane
false
Euclidean designs
design D
1984-01-01
block B
order n
block length
properties
behavior
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.
embedding
extensible design
relationship
269-277
block
https://scigraph.springernature.com/explorer/license/
paper
cardinality
article
asymptotic properties
design
https://doi.org/10.1007/bf00147650
plane
such embeddings
Asymptotic properties of locally extensible designs
length
uniqueness
asymptotic behavior
minimum block length
2022-11-24T20:45
projective plane
1984-01
doi
10.1007/bf00147650
dimensions_id
pub.1032889144
Mathematical Sciences
Springer Nature - SN SciGraph project
3
S. A.
Vanstone
15
Pure Mathematics