The paper reports the results of a search for pairs of groups of order $n$ that can be placed in the distance $n^2/4$ for the case when $n\in \{16,32\}$. The constructions that are used are of the general character and some of their properties are discussed as well.
@article{119240, author = {Natalia Zhukavets}, title = {On small distances of small 2-groups}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {42}, year = {2001}, pages = {247-257}, zbl = {1057.20018}, mrnumber = {1832144}, language = {en}, url = {http://dml.mathdoc.fr/item/119240} }
Zhukavets, Natalia. On small distances of small 2-groups. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 247-257. http://gdmltest.u-ga.fr/item/119240/
On the distance between distinct group Latin squares, J. Combin. Des. 5 (1997), 235-248. (1997) | MR 1451283 | Zbl 0912.05021
How far apart can the group multiplication table be?, European J. Combin. 13 (1992), 335-343. (1992) | MR 1181074
Non-isomorphic $2$-groups coincide at most in three quarters of their multiplication tables, European J. Combin. 20 (2000), 301-321. (2000) | MR 1750166
O Hammingově vzdálenosti grup, M.D. Thesis (in Czech), Charles University, Prague, 1998.
Close $2$-groups, Ph.D. Thesis, Charles University, Prague, in preparation.