A very successful antenna for VLF, LF and MF receive only is an E-field probe. Ideally these should be mounted outside the house with some experiments to find the quietest spot. Size is not important and these are much smaller than many antennas for much higher frequencies. The picture shows an example EFP. This is the complete antenna – no wires or loops etc are needed in addition. They can be made by just about anyone, so there is nothing stopping you having fun on 136,472 or even VLF RX. Some people have built these inside a short length of uPVC pipe. The important thing is they are very small and work well on the lower bands.
I have also used EFPs as mag mounts on the car when looking for my signal on 136kHz QRSS3. These are very compact antennas. PA0RDT has created a good design that many people are using.