TY - JOUR
T1 - The possible support sizes for BIB designs with ν = 8 and k = 4
AU - Hedayat, A.
AU - Stufken, J.
AU - Landgev, I. N.
N1 - Funding Information:
* Research is supported by Grant AFOSR 85-0320. + On leave from the University of Georgia, Department * Research is partly supported by NSC-Contract 37.
PY - 1989/7
Y1 - 1989/7
N2 - Hedayat and Hwang (J. Combin. Theory Ser. A, 36 (1984), 163-173) studied the support sizes for BIB designs with ν = 8 and k = 4. They established the existence or nonexistence for all possible support sizes, with the exceptions of 15, 16, 17, and 19. We will show that there are no such BIB designs with support sizes 15 and 16, while there are designs with support sizes 17 and 19. These latter designs require at least 42 blocks. In addition, we will provide an answer to their question on self-complementary designs.
AB - Hedayat and Hwang (J. Combin. Theory Ser. A, 36 (1984), 163-173) studied the support sizes for BIB designs with ν = 8 and k = 4. They established the existence or nonexistence for all possible support sizes, with the exceptions of 15, 16, 17, and 19. We will show that there are no such BIB designs with support sizes 15 and 16, while there are designs with support sizes 17 and 19. These latter designs require at least 42 blocks. In addition, we will provide an answer to their question on self-complementary designs.
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U2 - 10.1016/0097-3165(89)90051-4
DO - 10.1016/0097-3165(89)90051-4
M3 - Article
AN - SCOPUS:45149141920
SN - 0097-3165
VL - 51
SP - 258
EP - 267
JO - Journal of Combinatorial Theory, Series A
JF - Journal of Combinatorial Theory, Series A
IS - 2
ER -