This paper deals with techniques for finding $\Phi$-optimal designs for weighing $v$ objects in $b$ weighings using a spring balance. The optimality functions considered encompass a large class of functions. Results are applied to find $A$-, $D$- and $E$-optimal designs and the optimal designs obtained are seen to be related to certain types of well known block designs.
"On the Optimality of Spring Balance Weighing Designs." Ann. Statist. 11 (3) 970 - 978, September, 1983. https://doi.org/10.1214/aos/1176346262