Abstract-We adapt methods originally developed in information and coding theory to solve some testing problems. The efficiency of two-stage pool testing of items is characterized by the minimum expected number ( ) of tests for the Bernoulli -scheme, where the minimum is taken over a matrix that specifies the tests that constitute the first stage. An information-theoretic bound implies that the natural desire to achieve ( ) = ( ) as can be satisfied only if ( ) 0. Using random selection and linear programming, we bound some parameters of binary matrices, thereby determining up to positive constants how the asymptotic behavior of ( ) as depends on the manner in which ( ) 0. In particular, it is shown that for, where 0 1, the asymptotic efficiency of two-stage procedures cannot be improved upon by generalizing to the class of all multistage adaptive testing algorithms.