TY - JOUR
T1 - Extending symmetric designs
AU - Cameron, P. J.
PY - 1973/1/1
Y1 - 1973/1/1
N2 - If a symmetric 2-design with parameters (v, k, λ) is extendable, then one of the following holds: v = 4λ + 3, k = 2λ + 1; or v = (λ + 2)(λ2 + 4λ + 2), k = λ2 + 3λ + 1; or v = 111, k = 11, λ = 1; or v = 495, k = 39, λ = 3. In particular, there are at most three sets of extendable symmetric design parameters with any given value of λ. As a consequence, the only twice-extendable symmetric design is the 21-point projective plane.
AB - If a symmetric 2-design with parameters (v, k, λ) is extendable, then one of the following holds: v = 4λ + 3, k = 2λ + 1; or v = (λ + 2)(λ2 + 4λ + 2), k = λ2 + 3λ + 1; or v = 111, k = 11, λ = 1; or v = 495, k = 39, λ = 3. In particular, there are at most three sets of extendable symmetric design parameters with any given value of λ. As a consequence, the only twice-extendable symmetric design is the 21-point projective plane.
UR - http://www.scopus.com/inward/record.url?scp=0041744324&partnerID=8YFLogxK
U2 - 10.1016/0097-3165(73)90023-X
DO - 10.1016/0097-3165(73)90023-X
M3 - Article
AN - SCOPUS:0041744324
SN - 0097-3165
VL - 14
SP - 215
EP - 220
JO - Journal of Combinatorial Theory, Series A
JF - Journal of Combinatorial Theory, Series A
IS - 2
ER -