Self Orthogonal Latin Square Designs and their Importance

7 pages, 1 article*Self Orthogonal Latin Square Designs and their Importance* (Hedayat, A.) 7 page

Small Youden Rectangles, Near Youden Rectangles, and Their Connections to Other Row-Column Designs

In this paper we study Youden rectangles of small orders. We have enumerated all Youden rectangles for all small parameter values, excluding the almost square cases, in a large scale computer search. For small parameter values where no Youden rectangles exist, we also enumerate rectangles where the number of symbols common to two columns is always one of two possible values. We refer to these objects as \emph{near Youden rectangles}. For all our designs we calculate the size of the autotopism group and investigate to which degree a certain transformation can yield other row-column designs, namely double arrays, triple arrays and sesqui arrays. Finally we also investigate certain Latin rectangles with three possible pairwise intersection sizes for the columns and demonstrate that these can give rise to triple and sesqui arrays which cannot be obtained from Youden rectangles, using the transformation mentioned above.Comment: 33 pages, 21 Table

Two-fold triple systems without repeated blocks

AbstractDirect, easy, and self-contained proofs are presented of the existence of triple systems with λ = 2 having no repeated blocks