_:N8a18eca5cae646a9aa8eb1528ddc4984 .
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_:Na47b3b8e915b4bfeae1de878c9323b81 .
"1984-01" .
"S. A." .
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"plane" .
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"Department of Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada" .
"0046-5755" .
_:Na47b3b8e915b4bfeae1de878c9323b81 "3" .
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"design" .
"Asymptotic properties of locally extensible designs" .
"Euclidean designs" .
.
.
_:N8a42378d15d443e19f5b3a31f0ef881b "10.1007/bf00147650" .
"articles" .
"Pure Mathematics" .
"269-277" .
_:Nb250c775c3b34aa8a311ae213f909bf7 .
"Springer Nature" .
"1572-9168" .
"Vanstone" .
"block B" .
"Mullin" .
.
"cardinality" .
"order n" .
"https://doi.org/10.1007/bf00147650" .
_:N8a18eca5cae646a9aa8eb1528ddc4984 _:Naccdbdc66cfa413090267ff2174e105f .
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"block" .
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_:Nb250c775c3b34aa8a311ae213f909bf7 .
"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\u2282B*. 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." .
"Mathematical Sciences" .
.
_:N99e5987ef0ef4a0aaa4860f17dad3f46 "Springer Nature - SN SciGraph project" .
_:N99e5987ef0ef4a0aaa4860f17dad3f46 .
"Department of Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada" .
.
_:N8a42378d15d443e19f5b3a31f0ef881b .
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_:N8a18eca5cae646a9aa8eb1528ddc4984 .
_:Nea8b1f208c5f4aa487d93bdc84310d43 "15" .
_:Nea8b1f208c5f4aa487d93bdc84310d43 .
"properties" .
_:N99e5987ef0ef4a0aaa4860f17dad3f46 .
"finite projective plane" .
"St. Jerome's College, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada" .
"St. Jerome's College, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada" .
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"length" .
_:Naccdbdc66cfa413090267ff2174e105f .
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"Geometriae Dedicata" .
_:Nb250c775c3b34aa8a311ae213f909bf7 "pub.1032889144" .
_:Na47b3b8e915b4bfeae1de878c9323b81 .
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"article" .
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"extensible design" .
"asymptotic behavior" .
"projective plane" .
"relationship" .
_:N8a42378d15d443e19f5b3a31f0ef881b .
"R. C." .
"design D" .
_:N8a42378d15d443e19f5b3a31f0ef881b "doi" .
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"minimum block length" .
.
"1984-01-01" .
"block length" .
"such embeddings" .
_:Naccdbdc66cfa413090267ff2174e105f .
"uniqueness" .
"asymptotic properties" .
"https://scigraph.springernature.com/explorer/license/" .
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"embedding" .
.
.
"2022-12-01T06:18" .
"behavior" .
.