A new construction shows I2(n,4) = Ω(n^{3/2-o(1)}), improving the previous lower bound Ω(n^{4/3+o(1)}) for 2-parent-identifying set systems of block size 4.
In Coding Theory and Applications (Lecture Notes in Computer Science), vol
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On $2$-parent-identifying set systems of block size $4$
A new construction shows I2(n,4) = Ω(n^{3/2-o(1)}), improving the previous lower bound Ω(n^{4/3+o(1)}) for 2-parent-identifying set systems of block size 4.