Decomposable designs are important combinatorial designs, and have applications in constant weight codes, perfect threshold schemes and graph decompositions. Let be an even positive integer. A ‐decomposable super‐simple ‐balanced incomplete block design (BIBD) is a super‐simple ‐BIBD, , where , and each is a ‐BIBDs for . In this paper, for , it is proved that the necessary conditions for the existence of a ‐decomposable super‐simple ‐BIBD are also sufficient.
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Chen et al. (2022) studied this question.
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