function(Npop, nsamp, ne, LBalpha)

{

# a bisection routine to find a lower 1-alpha confidence bound for Ne, the number of population items in error.  Population size Npop, SRS size nsamp, ne = number of sample items in error.

            if(ne == 0) return(0) else {

                        Na <- ne

Pa <- (1 - phyper(ne - 1, Na, Npop - Na, nsamp))

if(Pa >= LBalpha)

                                    return(ne)

                        else {

                                    Nb <- Npop

                                    Pb <- 1

                                    while((Nb - Na) > 1) {

                                                Nnew <- trunc((Nb + Na)/2)

                                                Pnew <- (1 - phyper(ne - 1, Nnew, Npop - Nnew, nsamp))

                                                if(Pnew >= LBalpha) {

                                                  Nb <- Nnew

                                                  Pb <- Pnew

                                                }

                                                else {

                                                  Na <- Nnew

                                                  Pa <- Pnew

                                                }

                                    }

                                    if(Pa >= LBalpha)

                                                return(Na)

                                    else return(Nb)

                        }

            }

}