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Triples of orthogonal Latin and Youden rectangles for small orders
Author(s) -
Jäger Gerold,
Markström Klas,
Öhman LarsDaniel,
Shcherbak Denys
Publication year - 2019
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21642
Subject(s) - mathematics , combinatorics , enumeration , orthogonal array , orthogonal matrix , order (exchange) , pairwise comparison , orthogonal basis , projective plane , geometry , statistics , correlation , physics , taguchi methods , finance , quantum mechanics , economics
Abstract We have performed a complete enumeration of nonisotopic triples of mutually orthogonal k × n Latin rectangles for k ≤ n ≤ 7 . Here we will present a census of such triples, classified by various properties, including the order of the autotopism group of the triple. As part of this, we have also achieved the first enumeration of pairwise orthogonal triples of Youden rectangles. We have also studied orthogonal triples of k × 8 rectangles which are formed by extending mutually orthogonal triples with nontrivial autotopisms one row at a time, and requiring that the autotopism group is nontrivial in each step. This class includes a triple coming from the projective plane of order 8. Here we find a remarkably symmetrical pair of triples of 4 × 8 rectangles, formed by juxtaposing two selected copies of complete sets of mutually orthogonal Latin squares of order 4.