Group divisible designs with block size 4 and type g^um¹

Forbes, A. D. and Forbes, K. A. (2018). Group divisible designs with block size 4 and type g^um¹. Journal of Combinatorial Designs, 26(11) pp. 519–539.

DOI: https://doi.org/10.1002/jcd.21607

Abstract

Building upon the work of Wei and Ge (Designs, Codes,and Cryptography 74, 2015), we extend the range of positive integer parameters g, u, and m for which group divisible designs with block size 4 and type g^um¹ are known to exist. In particular, we show that the necessary conditions for the existence of these designs when m > 0 and m ≠ g are sufficient in the following cases: g ≡ 0 (mod 6), g =2 with one exception, 2⁶5¹, g =10, and g =11.

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