findsets.py

def find_sets(F,M,d, xRy):
    """
    Find M sets of d mutually orthogonal vectors from F (an iterable of vectors) so that each set is related pairwise by xRy
    """
    def xRY(v,W):
        """
        xRY(v,W) = is v related to every vector in W by the conditions you need

        We could just inline this function below, but the code below is a little more readable if we abstract it out
        """
        return all(xRy(v,w) for w in W)

    bases = []
    used = set() # we could also just keep track of the elements left if F is small enough
    for m in range(M):
        base = []
        for v in F:
            if tuple(v) in used:
                continue
            if all(v*w==0 for w in base) and all(xRY(v,S) for S in bases):
                base.append(v)
                used.add(tuple(v))
                if len(base)==d:
                    break
        else:
            # we went all the way through N, but didn't find enough vectors
            raise ValueError("couldn't find enough mutually orthogonal vectors")
        bases.append(base)
    return bases

I see that my code may not find a list of sets because once a mutually orthogonal set is found, it is fixed. Instead, the sets themselves should be re-examined too. So, for example, if that ValueError is raised, you'd have to backtrack and try a different list of sets.