This paper analytically characterizes certain classes of low-diameter strongly attack-tolerant networks of arbitrary size, which are globally optimal in the sense that they contain the minimum possible number of edges. Strong attack tolerance property of level <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$R$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>R</mi> </math> </EquationSource> </InlineEquation> implies that a...</equationsource></equationsource></inlineequation>