Existence of Five MOLS of Orders 18 and 60. Issue 4 (23rd December 2013)

• Record Type: Journal Article
• Authors: Julian, R.; Abel, R.
• Is Part Of: Journal of combinatorial designs. Volume 23:Issue 4(2015:Apr.)
• Page Start: 135
• Page End: 139
• Publication Date: 2013-12-23
• Subjects: Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21384
• Languages: English
• ISSNs: 1063-8539

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>In this article, we provide direct constructions for five mutually orthogonal Latin squares (MOLS) of orders <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjf85jgjd" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:10638539:media:jcd21384:jcd21384-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></alternatives></inline-formula> and 60. For <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjf85jggc" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:10638539:media:jcd21384:jcd21384-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mn>60</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>, these come from a new (60, 6, 1) difference matrix. For <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgjf85jghw" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:10638539:media:jcd21384:jcd21384-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mn>18</mml:mn></mml:mrow></mml:math></alternatives></inline-formula>, the required construction is obtained by combining two different methods that were used in the constructions of four MOLS(14) and eight MOLS(36).</p> </abstract>