The phrase “smallest information needed” refers to the least amount of data or facts required for a particular purpose. Here are some synonyms and an analysis of each:
Minimum essential information: This emphasizes that it is the bare minimum that is absolutely necessary. For example, “We only need the minimum essential information to make a decision.” It implies that anything more than this would be superfluous.
Necessary minimum data: This synonym clearly states that it is the data that is required and that it is the smallest amount possible. “The report should contain only the necessary minimum data.” It gives a sense of precision and economy in information gathering.
Bare minimum requirements: The term “requirements” suggests that these are the things that must be met. “We have to meet the bare minimum requirements of the project.” It implies that there is a baseline level of information that cannot be compromised.
Least amount necessary: This is a very straightforward way of expressing the concept. “We need to use only the least amount necessary of resources and information.” It emphasizes the idea of minimizing and being efficient with what is needed.
These synonyms can be used in different contexts to convey the idea of having only the smallest amount of information that is truly needed. They can help make your writing more precise and avoid unnecessary elaboration.