Why is the array used for a restricted hashing scheme always sized to a 4k + 3 prime? Why is the array used for a restricted hashing scheme always sized to a 4k + 3 prime? When they talk about a restricted hashing scheme are they talking about a non perfect hashing which includes having a collision algorithm which resolves that problem? Can someone please help me?
The mentioned scheme is the most probably Quadratic probing collision resolution in the Hash Table, so it is non-perfect.

The $4k + 3$ prime size of the table is to allow all cells to be probed, the size of different length will result in non accessible cells in the array, degrading performance and wasting space.

Please read about limitations of QP.