This analysis determines existence criteria for 1-rotational BIBDs with block size four, suggesting new design possibilities.
The necessary and sufficient conditions for the existence of 1‐rotational balanced incomplete block designs with block size four and index unity have been determined to be and [J. Comb. Theory, Ser. A 206 (2024) 105890]. This work completely determines the existence spectrum of 1‐rotational balanced incomplete block designs with block size four and any index . To be specific, for and , there exists a 1‐rotational BIBD if and only if , and .
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Zhang et al. (2026) studied this question.
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