full rank designs over Z_m

[Max Alekseyev]

SeqFans,

Does the following sounds familiar to anybody?

Fix an integer m>=2. For any positive integer n consider a matrix k x
n over Z_m such that any n rows (out of k) are linearly independent.
Define a(n) as the maximum possible k.

 From practical point of view such construction gives rise to a number
of sequences for different m. Are they in OEIS?

I'm also interested in the theory behind. I believe such matrices
should have been studied.

Thanks,
Max