Addendum to ``Construction of \((16,6)\)-configurations from a group of order 16'' by Gonzalez-Dorrego (Q1305059)

The author considers the construction of non-degenerate \((16,6)\)-configuration matrices, starting with a group \(F\) and \(16\) distinguished elements. This construction was introduced by \textit{M. R. Gonzalez-Dorrego} [J. Algebra 162, No. 2, 471--481 (1993; Zbl 0809.14031)]. In that paper initially it was supposed that only \(9\) constructions could be obtained in this way. The author proves here that in fact the complete list of constructions contains \(27\) sets of data.