Abstract :
(x,y,z)(x,y,z) is defined to be {(x,y),(y,z),(z,x)}{(x,y),(y,z),(z,x)} and is called a cyclically ordered 3-subset. A compatibly ordered orthogonal group divisible design (briefly, compatibly ordered-OGDD or COGDD) (X,G,A,B)(X,G,A,B) is a set X and a partition GG of X into classes (usually called groups), and two sets AA and BB of cyclically ordered 3-subsets of X (usually called blocks), so that (X,G,C,D)(X,G,C,D) is an orthogonal group divisible design, and if (a,b)(a,b) appears in a block of AA then (a,b)(a,b) appears in a block of BB, where C={{x,y,z}:(x,y,z)∈A}C={{x,y,z}:(x,y,z)∈A} and D={{x,y,z}:(x,y,z)∈B}D={{x,y,z}:(x,y,z)∈B}.
