For loops on a space

Dear Guys,

I want to compute the borders of a region. The region is like below:

R <= f1(p1,p2,p3,p4,p5,p6,p7,p8)

R <= f2(p1,p2,p3,p4,p5,p6,p7,p8)

over all p1, p2, p3, p4, p5, p6, p7, and p8 where p1+p2+p3+p4+p5+p6+p7+p8 = 1 (probability space)

So I have seven randoms in p1, p2 , p3, p4, p5, p6, and p7 (or seven degrees of freedom).

My problem is that I can not find a way to cover the whole space. To be brief,

I have given my code for the same problem with three degrees of freedom, where

R <= f1(p1,p2,p3,p4)

R <= f2(p1,p2,p3,p4)

over all p1, p2, p3, and p4 where p1+p2+p3+p4 = 1:

********

clear all

Rf = 0;

p1(1) = 0.00001;

p2(1) = 0.00001;

for j1 = 1:1:101

    if j1 > 1

    p1(j1) = 0.00001 + 0.004998*(j1-1);

    p2(j1) = 0.00001 + 0.004998*(j1-1);

    end

    p3(j1) = 1 - p1(j1) - p2(j1);

end

for i1 = 1:1:101

    for i2 = 1:1:101

          for i3 = 1:1:101

                            R1(i1,i2,i3) = f1 (p1(i1),p2(i2),p3(i3)) ;

                            R2(i1,i2,i3) = f2 (p1(i1),p2(i2),p3(i3)) ;

                            R(i1,i2,i3) = min(R1(i1,i2,i3),R2(i1,i2,i3));

                            Rf = max(R(i1,i2,i3),Rf);

                            if R(i1,i2,i3) > Rf

                               a1 = i1;

                               a2 = i2;

                               a3 = i3;

                            end

          end

    end

end

***************