A note on the huhwangwang conjecture for group testing

Hu et al. [A boundary problem for group testing, SIAM J. Algebraic Discrete Meth. 2 (1981), 8187] conjectured that the minimax test number to find d defectives in 3d items is 3d1, a surprisingly difficult combinatorial problem about which very little is known. In this article we state three more conjectures and prove that they are all equivalent to the conjecture of Hu et al. Notably, as a byproduct, we also obtain an interesting upper bound for M(d,n).