On the Classification of Resolvable 2-(12, 6, 5c) Designs
نویسندگان
چکیده
In this paper we describe a backtrack search over parallel classes with a partial isomorph rejection to classify resolvable 2-(12, 6, 5c) designs. We use the intersection pattern between the parallel classes and the fact that any resolvable 2-(12, 6, 5c) design is also a resolvable 3-(12, 6, 2c) design to effectively guide the search. The method was able to enumerate all nonsimple resolutions and a subfamily of simple resolutions of a 2-(12, 6, 15) design. The method is also used to confirm the computer classification of the resolvable 2-(12, 6, 5c) designs for c ∈ {1, 2}. A consistency checking based on the principle of double counting is used to verify the computation results.
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