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On an algorithm for a double-resolvability test. (English) Zbl 1199.05016

Summary: To find all doubly resolvable designs with definite parameters, we construct the design resolutions in lexicographic order point by point. To partial solutions with more than 2/3 of the points we apply a double-resolvability test, that means we try to construct an orthogonal resolution. The test reduces significantly the number of partial solutions, and is very important for the efficiency of the whole computation. We develop and compare two algorithms for a double-resolvability test. The first one implies the construction of the orthogonal resolution block by block (BB), while the second one does it class by class (CC). We present experimental results on the performance of both algorithms. Applying them, we also classify for the first time doubly resolvable \(2\)-\((16,4,2)\) and \(2\)-\((8,4,18)\) designs.

MSC:

05B05 Combinatorial aspects of block designs
05B15 Orthogonal arrays, Latin squares, Room squares
68R05 Combinatorics in computer science
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