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An SOLS (self-orthogonal Latin square) of order \(n\) with \(n_i\) missing sub-SOLS (holes) of order \(h_i\) (\(1 \leq i \leq k\)), which are disjoint and spanning (i.e., \(\sum_{i=1}^{k} n_ih_i = n\)), is called a frame SOLS and denoted by \(\text{FSOLS}(h_1^{n_1}, h_2^{n_2}, \ldots, h_k^{n_k})\).
In this article, it is shown that an \(\text{FSOLS}(3^{n-u}3^1)\) exists if and only if \(n \geq 4\) and \(n \geq 1 + \frac{2u}{3}\), with seventeen possible exceptions \((n, u) =\{(5, 1)\}\) and \(\{(n, u) = (n, \lfloor \frac{3(n-1)}{2}\rfloor)\) for \((n \in \{6, 10, 14, 18, 22, 30, 34, 38, 42, 46, 54, 58, 62, 66, 70, 94\}\)\}.