There is no such thing as a 'small' Koi pond. If there were, we'd have a far bigger market than we do.
Koi are fish that are the elephant of the ornamental fish world. You cannot keep an elephant in a mouse cage - it is cruel to attempt to do so.
Koi do not grow to the size of the pond they are in. Koi are selectively bred carp that have been many generations in the making with size being the single most important criterion, even before pattern.
A typical Koi bred today can expect a minimum size of 65 to 70cm with the vast majority exceeding 75cm and heading well over 85cm when fully grown, which can be in as little as 7 or 8 years.
This is a massive fish. It cannot be reasonably expected to live in a bath tub. Not can it be reasonably expected to live on a starvation diet.
As a Koi owner you have the responsibility to ensure the well being of your Koi. This requires a Koi pond of suitable size along with suitable filtration that can cater for your pet.
A Koi pond should not be anything less than 10 000 litres.There should never be more than 10 Koi in this pond at any time, IRRESPECTIVE of size!
Filtration should be sufficient to cater for 10 full grown adult Koi! This cannot be achieved with small filters. Simple physics dictates you need space and you need capacity. Small filters simply cannot have the physical capacity required.
Koi keeping is, as a result, not a cheap hobby. You need to be fully aware that it is not a fad, it is a multi decade long commitment you are undertaking. Go in with your eyes wide open!