Some solutions for n=3 k=3
..0..0..0..0..1..2....0..0..0..1..0..2....0..0..0..1..0..1....0..0..0..1..2..1
..0..2..3..0..2..1....0..2..0..0..2..3....0..2..0..0..2..0....0..2..0..0..0..0
..0..0..2..0..1..0....0..0..2..0..0..2....0..0..2..0..0..1....0..0..2..1..2..0
..1..0..1..0..2..1....1..0..1..3..0..1....1..0..1..2..0..2....1..0..1..2..3..0
..0..0..0..0..1..3....0..0..0..0..0..3....0..0..0..0..0..1....0..0..0..0..0..0
..0..0..2..3..0..1....0..0..2..3..1..0....0..0..2..1..3..2....0..0..2..3..2..3