Semi-Latin squares with side six and block size three, constructed by superimposing each of the 9408 reduced Latin squares of order six on each of certain semi-Latin squares, are here presented. A Microsoft Excel program was used to facilitate the construction by superposition and the statistical evaluation of the corresponding semi-Latin squares of sides six in blocks of size three by computing their A, D, E and MV statistical efficiency measures. A total of 65856 Semi-Latin squares with side six and blocks of size three where constructed. A semi-Latin square with side six and block size three was identified to be A-optimal, D-optimal, E-optimal and MV-optimal. Also, with respect to the efficiency measures, the same optimal semi-Latin square is the most efficient of the 65856 Semi-Latin squares. This efficient semi-Latin square having canonical efficiency factors, 0.5980 with multiplicity three, 0.6667 with multiplicity ten, 0.8464 with multiplicity three and 1.0 with multiplicity one, is a simple orthogonal multi-array (SOMA) of order six; specifically, SOMA(3, 6). This optimal and efficient semi-Latin square has the same A, D, E and MV statistical efficiency values with the two indecomposable SOMA(3, 6) developed by Soicher and an efficient semi-Latin square of order six by Bailey.