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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics