s(P,Q) is the sum of dot products of vectors P and Q in each dimension.  The 0 dot product indicates that the vectors must be orthogonal to each other. 
In a n-dimensional space, we have n axes  orthogonal to each other.  It is given that for every pair the dot product must be 0, then at most n vectors each mentioning each dimension can be considered.  Thus for 10 dimensional space’s set of vectors ℒ , 10 mutually orthogonal vectors can be present.