This is a well studied problem. Dan Bernstein famously used constant databases with guaranteed performance in tinydns en qmail:

• https://cr.yp.to/cdb.html
• https://en.wikipedia.org/wiki/Cdb_(software)

CDB and deratives use a external file for the k-v content, but there is no need to do this if the number a entries is very small.

Some papers that describe the algorithms en the math:

• https://cmph.sourceforge.net/papers/chm92.pdf (old, but very good introduction)
• https://www.netbsd.org/gallery/presentations/joerg/asiabsdcon2013/hashing.pdf (everyhting since then)