The notion of general balance due to Nelder is discussed in relation to the eigenvectors of an information matrix, combinatorial balance and the simple combinability of information from uncorrelated sources in an experiment.
"Balance in Designed Experiments with Orthogonal Block Structure." Ann. Statist. 11 (4) 1069 - 1085, December, 1983. https://doi.org/10.1214/aos/1176346322