A 2-(22, 8, 4) Design Cannot Have a 2-(10, 4, 4) Subdesign

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Abstract

The smallest BIBD, as for the number of points and blocks, whose existence is still undecided is 2-(22, 8, 4). Possible subconfigurations of such a design, namely 2-(10, 4, 4) designs, are here ruled out. The result is obtained by classifying all 2-(10, 4, 4) designs and trying to find 2-(22, 8, 4) designs by solving instances of the maximum clique problem.

BIBD - codes of designs - maximum clique problem

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A 2-(22, 8, 4) Design Cannot Have a 2-(10, 4, 4) Subdesign

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Abstract

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