Max 4x1 pattern fit within 11x11 area

Question

Rimworld is a tile-based videogame. There is a constructible called a sun lamp, which provides light for indoor farming:

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As you can see, the area covered by the lamp is 11 * 11, minus 1 for the lamp itself, minus 4 corners * 5 tiles not covered in each corner. That's 11*11-1-4*5 = 121-1-20 = 100 tiles total.

There is another constructible you can see in this image, the hydroponics basin, which provides superior soil. It covers a 4*1 area.

The current optimized setup is also shown in this image: 24 basins cover 96 tiles of a sun lamp's area. The question is: is there a way to fit 25 in, covering all the tiles?

Answer 1

The answer is:

No.

Why?

Because imagine the farm is a checkerboard. Then we have $(3+4+5+6+5)\times2+6=52$ squares of one colour, say black. Each hydroponic basin covers exactly $2$ black and $2$ white squares. As there are only $48$ white squares, $24$ is the most we can fit in.