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We call a real multi-dimensional array a {\em tensor} for short. Inenumerating vertices of the polytopes of stochastic tensors, differentapproaches have been used: {(1)} Combinatorial method via Latin squares; {(2)}Analytic (topological) approach by using hyperplanes; {(3)} Computationalgeometry (polytope theory) approach; and (4) Optimization (linear programming)approach. As all these approaches are worthy of consideration and investigationin the enumeration problem, various bounds have been obtained. This note is tocompare the existing upper bounds arose from different approaches.

Comparison of the upper bounds for the extreme points of the polytopes of line-stochastic tensors