On the existence of super-simple designs with block size 4 |
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Authors: | Peter Adams Darryn E Bryant A Khodkar |
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Institution: | (1) Centre for Combinatorics, Department of Mathematics, The University of Queensland, 4072 Queensland, Australia |
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Abstract: | Summary We prove that forv = 1 and for allv 1 (mod 3),v 10, there is a (v, 4, 4) design with the property that no triple appears in more than one block. The proof of this result is made more difficult by the non-existence of a GDD (4, 4, 3; 15) with no triple appearing in more than one block. We also show that forv = 1 and for allv 1, 4 (mod 12),v 13, there is a (v, 4, 2) design with this property, and with the additional property that the design is the union of two (v, 4, 1) designs. |
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Keywords: | Primary 05B05 |
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