Geodesic
Nonabelian groups with \((96,20,4)\) difference sets
The electronic journal of combinatorics, Tome 14 (2007)
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We resolve the existence problem of $(96,20,4)$ difference sets in 211 of 231 groups of order $96$. If $G$ is a group of order $96$ with normal subgroups of orders $3$ and $4$ then by first computing $32$- and $24$-factor images of a hypothetical $(96,20,4)$ difference set in $G$ we are able to either construct a difference set or show a difference set does not exist. Of the 231 groups of order 96, 90 groups admit $(96,20,4)$ difference sets and $121$ do not. The ninety groups with difference sets provide many genuinely nonabelian difference sets. Seven of these groups have exponent 24. These difference sets provide at least $37$ nonisomorphic symmetric $(96,20,4)$ designs.
DOI : 10.37236/927
Classification : 05B10 
@article{10_37236_927,
     author = {Omar A. AbuGhneim and Ken W. Smith},
     title = {Nonabelian groups with \((96,20,4)\) difference sets},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/927},
     zbl = {1110.05015},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/927/}
}
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Omar A. AbuGhneim; Ken W. Smith. Nonabelian groups with \((96,20,4)\) difference sets. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/927

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