Loops, Latin Squares and Strongly Regular Graphs: An Algorithmic Approach via Algebraic Combinatorics

Using in conjunction computer packages GAP and COCO we establish an efficient algorithmic approach for the investigation of automorphism groups of geometric Latin square graphs. With the aid of this approach an infinite series of proper loops is presented which have a sharply transitive group of collineations. The interest in such loops was expressed by A. Barlotti and K. Strambach.

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