Make Displacement map

I am trying to make this texture in blender for a flip flop for presentation , my current result is quite jaggered, what is the correct way in creating the map for this? I drew it up in illustrator and used that image and from my research i have found that there is not enough height information(i stand to be corrected)

What I am trying to achieve:
image

My current Displacement Map:

My Current Result:

as you notice it starts bluring out and becoming quite jaggered,

Displacement is in need of real geometry. So if the height offset isnt visible you may just want to use a normal map instead. Otherwise subdivide the mesh.

Beside that your image is pure black and white. Blur the image itself a bit to get a less pixelated border on the displacement itself and make sure you use smooth shading.

Thank you for the reply. i did try the blurred image but it did not quite work. HOWEVER, the image you blurred works like magic. can i ask how much you blurred it by?

Make sure you use a blur operator that works across the edges. In Krita, hit Shift+W prior to blurring to enable WrapAround Mode. Not sure how this works in other software.