very cheap bus communication network
If you really only want one bit per LED and you are organising the LEDs as strips, a shift register may be the way to go.

Those are not too expensive, and you only need two or three wires for N bits. They work by shifting the bits into the register one by one and then giving a signal that the new bit values shall be applied to the outputs. You may need additional transistors or LED drivers if the shift register cannot source the current needed for the LEDs (likely if those LEDs are any bright).

Depending on the driver you use, &lt; 1 EUR per LED should easily be possible.

WS2812-based LED strips are more versatile and sold at different shops, you should be able to find them. In the end, those are probably even cheaper than a home-brew solution, but if you’re in it for the learning, you might want to consider home-brewing it anyways.