Is there a way to generate 256 equations of the form

Eq256:= {e1>0,e2>0,e3>0, e4>0,e5>0 e6>0,e7>0,e8>0}
Eq255:= {e1>0,e2>0,e3>0, e4>0,e5>0 e6>0,e7>0,e8<0}
.
.
Eq1:= {e1<0,e2<0,e3<0, e4<0,e5<0 e6<0,e7<0,e8>0}
Eq0:= {e1<0,e2<0,e3<0, e4<0,e5<0 e6<0,e7<0,e8<0}

The < can be thought of as a binary 0 and the > as a binary 1 so there are 2^8 equations.

I want to call a procedure that does the above with something like

For i = 1 to 256 do
eq:=getequ(i):# getequ:=proc(i) returns the automatically generated equation
LinearUnivariateSystem(eq,x);
end do;


I can do it all by hand but what a pain.

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