Toward the continuum limit of BK with the quenched Kogut-Susskind quark action

We present new results of our ongoing project toward a precision determination of the kaon B parameter with the Kogut-Susskind quark action in quenched QCD. New results taken at β=6.4 and β=5.7 suggest that an apparently linear a dependence of BK previously observed for β=5.85-6.2 arises from a change of curvature from convex to concave as the lattice spacing is reduced. Fitting data for β ≥ 5.93 with an O(a2) form yields BK(NDR,2 GeV)=0.587(7)(17) in the continuum limit. We also describe a finite-size study of BK at β=6.0 and 6.4, and a reanalysis of the theoretical argument for O(a2) behavior. (orig.)