  The two-particle correlation obtained from the quantum state used in the Bell
inequality is sinusoidal, but the standard Bell inequality only uses two pairs
of settings and not the whole sinusoidal curve. The highest to-date visibility
of an explicit model reproducing sinusoidal fringes is 2/pi. We conjecture from
a numerical approach presented in this paper that the highest possible
visibility for a local hidden variable model reproducing the sinusoidal
character of the quantum prediction for the two-particle Bell-type interference
phenomena is 1/sqrt2. In addition, the approach can be applied directly to
experimental data.
