Some non-isomorphic \((4t+4,8t+6,4t+3,2t+2,2t+1)\)-BIBD’s. (English) Zbl 0756.05015
Summary: The automorphism groups of parts of the \((4t+3,\;2t+1,t)\)-BIBD’s are studied in order to show that these designs can be used to construct a great many non-isomorphic \((4t+4\), \(8t+6\), \(4t+3\), \(2t+2\), \(2t+1)\)-BIBD’s if certain conditions are met. In particular,
92,436,200 non-isomorphic (16, 30, 15, 8, 7)-BIBD’s, 10,869,917,004,894,316 non-isomorphic (20, 38, 19, 10, 9)-BIBD’s, 403,880,965,784,264,348 non-isomorphic (24, 46, 23, 12, 11)-BIBD’s, 9,820,329,245,540,352,000,000 non-isomorphic (28, 54, 27, 14, 13)-BIBD’s, and
38,029,083,844,041,728,836,746,735,484 non-isomorphic (32, 62, 31, 16, 15)-BIBD’s are constructed.
92,436,200 non-isomorphic (16, 30, 15, 8, 7)-BIBD’s, 10,869,917,004,894,316 non-isomorphic (20, 38, 19, 10, 9)-BIBD’s, 403,880,965,784,264,348 non-isomorphic (24, 46, 23, 12, 11)-BIBD’s, 9,820,329,245,540,352,000,000 non-isomorphic (28, 54, 27, 14, 13)-BIBD’s, and
38,029,083,844,041,728,836,746,735,484 non-isomorphic (32, 62, 31, 16, 15)-BIBD’s are constructed.
MSC:
| 05B05 | Combinatorial aspects of block designs |
| 05B20 | Combinatorial aspects of matrices (incidence, Hadamard, etc.) |
References:
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