Explicit asymptotic formulas for sample size as function of lot size and for accepe ante number as function of sample size are derived for the Dodge-Romig LTPD single sampling inspection plans. Numerical investigations show that a simple finite population correction of the asymptotic formulas leads to a good approximation to the Dodge-Romig solution. Tables and graphs are provided for the asymptotic solution. Asymptotic formulas are also given for the producers risk and for the minimum amount of inspection for lots of process average quality. The main results are that sample size asymptotically is proportional to the logarithm of lot size and that the highest allowable fraction defective in the sample converges to the tolerance fraction defective, the difference being of order 1/√n.