I recently hit the roof for maximum texture size for my opengl implementation (GL_MAX_TEXTURE_SIZE contains $3379$) when I wanted to create a texture for a 4k resolution video frame ($3840 \times 2160$).
This made me think about various ways to circumvent the problem that $3840>3379$.
I have used TEXTURE_2D_ARRAY, and I suppose one way would be to create such an array with sizes divided by two. In my case 4 slices of $1920\times 1080$ which then get to represent one "quadrant" each. Like a "block-matrix", so to speak.
I was thinking maybe there exist other, better solutions of how to address this.