Existence of 2 SOLS and 2 ISOLS

In this paper, we investigate the existence of two self-orthogonal Latin squares of order vv (2-SOLS(v)). It is found that 2-SOLS(v) exist for all v≥7v≥7 except possibly for v∈{10,12,14,18,21,22,24,30,34}v∈{10,12,14,18,21,22,24,30,34}. A number of sets of 2 incomplete SOLS (2 ISOLS) (and hence also 4 incomplete mutually orthogonal Latin squares, briefly 4 IMOLS) are also given.