Sufficient conditions for balanced incomplete block designs to be minimal fractional combinatorial treatment designs

Sufficient conditions are given for balanced incomplete block designs with block sizes three and four to be saturated minimal fractions of m items taken in mixture sizes of n = 3 and 4 for estimating the contrasts of item means and twoitem specific mixing effects.Such fractions are useful for investigations involving mixtures of crops, drugs, marketing practices and other systems using mixtures of items. The balanced incomplete block design with parameters (nu)= 6 and k = 4 is shown to be a saturated minimal fraction for estimating contrasts of item means and two-item and threeitem specific mixing effects. This is a continuation of the work of Federer & Raghavarao (1987) and Federer (2001).