The study of \((n\times m,k,\lambda _a,\lambda _c)\)-geometric orthogonal codes (\((n\times m,k,\lambda _a,\lambda _c)\)-GOCs) is motivated by the application in DNA origami. The central research on GOCs is to determine the value of \(\Phi (n\times m,k,\lambda _a,\lambda _c)\), i.e., the largest possible size among all \((n\times m,k,\lambda _a,\lambda _c)\)-GOCs. When \(\lambda _a=\lambda _c\), the exact values of \(\Phi (n\times m,3,1,1)\) and \(\Phi (n\times m,k,k-1,k-1)\) were recently determined by Wang and Su et al. In this paper, we research on the cases of \(\lambda _c=k-1\) and \(\lambda _a \le k-2\). We determine the exact values of \(\Phi (n\times m,k,k-2,k-1)\) and \(\Phi (n\times m,k,k-3,k-1)\), and give a calculation method of \(\Phi (n\times m,k,\lambda _a,k-1)\) with \(\lambda _a\le k-4\) for any positive integers n, m and k.