General balance and treatment permutations

Many equi-replicate designs, whether ordinary block designs or multi-stratum designs, have a structure which is left unchanged by a group G of permutations of the treatments. This group G is often used in the construction of the design. A survey of the properties of such designs is given, and useful necessary conditions on G are found for such a design to be generally balanced. If G is Abelian, then the necessary conditions are satisfied: in this case explicit formulas for the efficiency factors are given.