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The 2-(9, 4, 3) and 3-(10, 5, 3) designs
Authors:DR Breach
Institution:Department of Mathematics, University of Canterbury, Christchurch, New Zealand
Abstract:It is shown that there is a unique 2-(9, 4, 3) design with three different extensions to a 3-(10, 5, 3) design. Two of the extensions are isomorphic and have a further extension to the unique 4-(11, 6, 3) design. There is another 2-(9, 4, 3) design with just two extensions to a 3-design. There are 11 2-(9, 4, 3) designs in all, as announced by van Lint, et al. and Stanton et al. There are seven 3-(10, 5, 3) designs of which one is triply transitive, another transitive, and the rest are not transitive but are self-complementary. The transitive 3-designs each have one restriction to a 2-design. Of the non-transitive 3-designs 4 each have two restrictions and the fifth has three.
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