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:
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).