No entry greater than 1 in absolute value

 [-1  -1   1; -1  -1  -1; -1   1  -1;  1  -1  -1]      2 2 2
 [-1   1  -1; -1  -1  -1; -1   1   1;  1   1  -1]      2 2 2
 [-1   1  -1; -1  -1   1;  1  -1  -1; -1  -1  -1]      2 2 2
 [-1   1  -1; -1   1   1; -1  -1   1; -1  -1  -1]      2 2 2
 [-1  -1  -1;  1  -1   1; -1   1   1; -1  -1   1]      2 2 2
 [-1  -1  -1; -1   1  -1; -1  -1   1; -1   1   1]      2 2 2
 [-1   1   1;  1  -1   1; -1  -1   1;  1   1   1]      2 2 2
 [-1   1   1;  1   1  -1; -1   1  -1;  1   1   1]      2 2 2
 [-1   1  -1;  1   1   1;  1   1  -1; -1   1   1]      2 2 2
 [ 1  -1  -1;  1   1   1; -1   1  -1;  1   1  -1]      2 2 2
 [ 1  -1  -1;  1   1  -1;  1   1   1;  1  -1   1]      2 2 2
 [ 1   1   1; -1   1   1;  1   1  -1; -1   1  -1]      2 2 2
 [ 1   1   1;  1   1  -1; -1   1   1;  1  -1   1]      2 2 2
 [ 1  -1  -1; -1  -1   1; -1   1  -1; -1  -1  -1]      2 2 2
 [ 1  -1   1; -1   1   1;  1   1   1;  1   1  -1]      2 2 2
 [ 1  -1  -1;  1   1   1;  1  -1   1; -1  -1   1]      2 2 2
 [ 1  -1  -1; -1   1  -1;  1   1  -1;  1   1   1]      2 2 2
 [ 1  -1   1; -1  -1  -1;  1  -1  -1;  1   1  -1]      2 2 2
 [ 1  -1   1; -1  -1  -1; -1  -1   1;  1  -1  -1]      2 2 2
 [ 1  -1  -1;  1   1   1; -1  -1   1;  1  -1   1]      2 2 2

No entry greater than 2 in absolute value

 [-2  -2   1;  2   2  -1;  2   2  -1;  2   2  -1]      6 0 0
 [ 1   2   2; -1  -2  -2;  1   2   2; -1  -2  -2]      6 0 0

 [-1  -1  -2; -2   2  -2; -1  -1   2; -2   2   2]      4 4 2
 [-2  -2   1;  2   2   1;  2  -2  -1;  2  -2   1]      4 4 2
 [ 2   1  -1;  2  -2  -2;  2   2   2; -2   1  -1]      4 4 2
 [-2  -2   1;  2  -2   1; -2  -2  -1;  2  -2  -1]      4 4 2
 [ 2   2  -1;  2  -2   1; -2   2   1; -2  -2  -1]      4 4 2
 [-1  -2   1;  2  -2   2; -2  -2  -2; -1   2   1]      4 4 2
 [ 1   1   2; -1   1   2;  1   1  -2; -1   1  -2]      4 2 2
 [ 1  -2  -2; -1  -1   1; -1  -2  -2; -1   1  -1]      4 2 2
 [-1  -1  -1; -1   2  -2;  1  -1  -1; -1  -2   2]      4 2 2
 [ 2   2  -1;  2   2   1; -1   1  -1;  1  -1  -1]      4 2 2
 [ 1   2   2;  1  -2  -2;  1   1  -1;  1  -1   1]      4 2 2
 [ 2  -2  -1; -1  -1   1;  1   1   1;  2  -2   1]      4 2 2
 [ 2  -2  -2; -2  -2   2;  1   2   1; -1   2  -1]      4 4 2
 [-2   1   2;  2  -1   2;  2   1   2; -2  -1   2]      4 4 2
 [ 2  -2   2; -2  -1  -1;  2  -1  -1; -2  -2   2]      4 4 2
 [ 2   1   1;  2  -2   2; -2   1   1; -2  -2   2]      4 4 2
 [-1   2   1; -1  -2  -1; -1   2  -1; -1  -2   1]      4 2 2
 [-2  -2  -2; -2   2   2; -2   2  -2; -2  -2   2]      4 4 4

Of these, [-1 2 1; -1 -2 -1; -1 2 -1; -1 -2 1] and [-2 1 2; 2 -1 2; 2 1 2; -2 -1 2], has nice U and V matrices.

No entry greater than 3 in absolute value

 [ 2   1  -2; -2  -1   2; -1  -1   3;  3   1  -1]      6 2 0
 [-2   2  -2; -2  -3   3;  2  -2   2; -2  -1   1]      6 4 0
 [-3   3  -3;  1  -3  -1;  1  -1   1; -1  -1  -3]      6 4 0
 [-2  -2   1; -2   2   3;  2  -2  -3;  2   2  -1]      6 4 0
 [ 2   2  -3;  2   2  -3; -2   2   1;  2  -2  -1]      6 4 0
 [-3   2   2; -1   2  -2; -1   2  -2;  3  -2  -2]      6 4 0
 [ 3  -2   2;  3   1  -1; -3   2  -2;  3   3  -3]      6 6 0

 [ 1  -1   3;  1   2  -2;  2  -2   1;  2   1   2]      5 3 2
 [-1   2  -2; -2  -2   3;  2  -1  -2; -1  -1  -1]      5 3 2
 [ 3  -2  -2; -2  -1  -2;  2   2  -3;  3   3   3]      6 5 3
 [-3  -3   3; -2  -2  -1; -2   1   2;  1  -2   2]      6 3 3
 [-1  -2   2; -2   1   2; -3  -1   1; -2  -2  -1]      5 3 2
 [-2   1   2;  2   2   1;  1  -2   2; -3  -3   3]      6 3 3
 [ 2   2  -3; -1   1  -3; -1   1   3;  2   2   3]      6 4 2
 [-2   1   2;  1  -2   2;  3  -3   3;  2   2   1]      6 3 3
 [-2  -3  -3;  2   1   1;  2  -3  -1;  2  -1  -3]      6 4 2
 [-1  -3   1;  1  -3  -3;  3  -3  -1;  3   3  -3]      6 6 2
 [ 2   3  -1; -2   1  -1; -2   3  -3; -2  -1   3]      6 4 2
 [ 2  -3   1;  2   1  -1;  2  -1   3;  2   3  -3]      6 4 2
 [ 3  -3   3; -1  -1   3; -1  -1  -3;  3  -3  -3]      6 6 2

No entry greater than 4 in absolute value

 [ 4  -4   4;  1  -1  -1; -1   1   1;  1  -1  -3]      7 4 0

 [-1  -4   1; -2  -1   1;  2  -2  -2;  1   1  -2]      5 4 1
 [ 2   1  -4;  1   3   1;  1  -2  -2; -2  -4  -1]      6 5 1
 [-1   1  -4; -4   2   4; -1   4   1; -4  -1  -1]      7 5 4
 [ 2  -3  -1; -3  -2  -3;  1   3  -2;  2   4   2]      7 4 3
 [ 1  -2  -4;  2   1   2;  4  -2   1;  3  -3   3]      7 5 2
 [ 4   2   2; -1   2   2; -2   4  -1; -2   3  -4]      7 5 3
 [ 2   4  -1; -1  -2  -2;  3   3   3;  2  -1  -4]      7 5 2
 [ 2  -2  -3; -2   3   2; -2  -4   2;  3  -2  -2]      7 5 1
 [ 4  -1   2;  2   2  -4; -3   4  -2; -2  -2  -1]      7 5 3
 [-2   4  -1; -2   4  -2; -2   2   4;  1   2   2]      7 5 2
 [ 2   2   1;  2  -2  -4; -1  -4   2; -4   3   2]      7 5 3
 [-4  -3  -2; -2   2   1; -3   3   3;  3   4  -2]      7 6 3
 [ 4  -2   1;  2  -1  -2; -2  -4  -2; -3   2   4]      7 5 3
 [ 1  -4   1;  2  -4  -2; -1  -4  -1; -2  -4   2]      8 4 2
 [-4   4  -4;  2  -1   1;  1  -1   2; -1   2  -1]      8 1 1
 [-4  -2  -2; -4  -4  -1; -2  -4  -2; -4  -4   4]     10 5 2
 [-2   4   2; -4   4  -4; -4   4   1;  4  -2  -2]     10 5 2
 [ 3  -3   3;  2  -3   4;  3  -2   4; -2   2  -3]     10 1 1
 [-4  -3  -4;  3   4   4; -2  -2   4; -4  -4  -3]     11 5 1

No entry greater than 5 in absolute value

 [ 3   5   2;  2   3   1; -2  -4  -2; -1   2   3]      9 3 0

 [-1   4   4; -4  -1   2;  4  -2   5; -4  -2   2]      7 7 5
 [ 1  -4   4;  2   2   5;  2  -3   2;  3   5  -3]      9 6 3
 [ 2  -4  -5; -4   4  -4;  3   2  -2; -2  -5   4]      9 7 5
 [-4  -2  -1;  5   5   5;  2  -2   4; -4   2   1]     10 5 4
 [ 1   1  -1;  5  -1   5;  4  -4  -4; -5  -1  -5]     10 7 2
 [ 3   3  -5;  1   3   3;  5  -5  -5;  3  -5   3]     10 8 4