Abstract
We give the explicit construction of a regular (17q, 17, 2)-BIBD for any prime power q ≡ 17 (mod 32) such that 2 is not a 4th power in GF(q) and the explicit construction of a regular (25q, 25, 3)-BIBD for any prime power q ≡ 25 (mod 48) such that \(\sqrt 3\) and \(\sqrt 3\)+3 are non-squares in GF(q).
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Buratti, M. Some (17q, 17, 2) and (25q, 25, 3) BIBD Constructions. Designs, Codes and Cryptography 16, 117–120 (1999). https://doi.org/10.1023/A:1008384912209
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DOI: https://doi.org/10.1023/A:1008384912209