In the linear space of all real $n \times n$ matrices, find the maximum possible dimension of a linear subspace $V$ such that $$ \forall X, Y \in V \quad \operatorname{trace}(X Y)=0 $$ (The trace of a matrix is the sum of the diagonal entries.) Please provide the value of the answer when $n = 8$. The answer should be in the format \frac{m}{n}, directly give the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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