Is there a name for this given type of matrix? Given a finite set of symbols, say $\Omega=\{1,\ldots,n\}$, is there a name for an $n\times m$ matrix $A$ such that every column of $A$ contains each elements of $\Omega$?
(The motivation for this question comes from looking at $p\times p$ matrices such that every column contains the elements $1,\ldots, p$).

A sensible definition for this matrix would be a column-Latin rectangle, since the transpose is known as a row-Latin rectangle.  Example:

A. Drisko, Transversals in Row-Latin Rectangles, JCTA 81 (1998), 181-195.

The $m=n$ case is referred to as a column-Latin square in the literature (this is in widespread use).
I found one example of the use of column-Latin rectangle here (ref.; .ps file).
