Existence of Five MOLS of Orders 18 and 60. Issue 4 (23rd December 2013) - Julian, R.; Abel, R.
Abstract In this article, we provide direct constructions for five mutually orthogonal Latin squares (MOLS) of orders <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjf85jgjd" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />v=18</alternatives> and 60. For <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjf85jggc" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />v=60</alternatives>, these come from a new (60, 6, 1) difference matrix. For <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjf85jghw" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />v=18</alternatives>, the required construction is obtained by combining two different methods that were used in the constructions of four MOLS(14) and eight MOLS(36).