How to find "sparse" orthonormal vectors to some matrix A?

Question

Assume we have an n by p matrix $A$, where $n>p$ (and assume $A$ is of rank p). I'd like to find $n-p$ orthonormal vectors (each of length n), that are orthogonal to A. Questions:

1. What are the common processes to find such vectors?

2. I'd like these vectors to be as sparse as possible (i.e.: to have as many 0 values as possible). Is there a preferred method for getting that behavior from the process proposed in 1?

Thanks.