A series of triplet objectives have been corrected to the same third-order values and compared by computing the fifth-order aberrations. The calculations show that the most symmetrical solutions have reduced fifth-order coma but have an inward curving, high-order astigmatism.
ROBERT E. HOPKINS, "Third-Order and Fifth-Order Analysis of the Triplet," J. Opt. Soc. Am. 52, 389-393 (1962)