The combinatorial designs whose sizes achieve the Fisher type lower bounds are called tight, and it has been conjectured that the only tight combinatorial designs with strength at least 3 are Witt designs. In this talk, I will discuss finiteness of such tight designs, and give an explicit bound for the parameters. A key step in the proof is to reduce the problem down to a complicated Diophantine equation. I will also discuss methods to solve such Diophantine equations arising from classifications of combinatorial structures.