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Nicole Saeed: The search for orthogonal Latin squares

Time: Wed 2021-12-15 11.00 - 12.00

Location: Zoom: 632 1515 7930, contact to get the password

Respondent: Nicole Saeed

Abstract: Latin squares are n×n arrays where the elements in each row and column do not repeat; mutually orthogonal Latin squares (MOLS) are sets of Latin squares such that, when their elements are superimposed on top of each other, all element combinations are unique. This thesis explains the relationship between MOLS and finite projective plane geometry by detailing how one might construct a finite projective plane from a finite field as well as how a finite projective plane may be used to construct a set of MOLS and viceversa. With the link between MOLS and finite geometries established, some examples of proofs showing the non-existence of a finite projective plane of certain orders are discussed.