LinZip interpolation constantly fails with some input in small characteristic

[PoslavskySV]

LinZip makes too many loop cycles (system is UnderDetermied) with Vandermonde powers ((evaluationPoint) ^ (iTry)). The answer will not be even obtained if NUMBER_OF_UNDER_DETERMINED_RETRIES is too small (each evaluation (evaluationPoint) ^ (iTry) will give underdetermined system). Test case:

@Test
public void testSmallDomain2() throws Exception {
    lIntegersModulo domain = new lIntegersModulo(3);
    String[] vars = {"a", "b", "c", "d", "e"};

    lMultivariatePolynomialZp arr[] = {
            lMultivariatePolynomialZp.parse("1+2*c^3*d^2+2*b^3*c^3*d^3*e+a*c^3*d*e+2*a^2*b^3*c^2*d^2*e^3+a^2*b^3*c^3*e^2", domain, vars),
            lMultivariatePolynomialZp.parse("1+b^3*c^2*d^3*e^3+a*c^3*d*e^2+2*a^3*e^3+2*a^3*b^3*d*e^3+2*a^3*b^3*c*d^3*e", domain, vars),
            lMultivariatePolynomialZp.parse("1+2*a*b^3*c+a^2*d^3*e", domain, vars),
            lMultivariatePolynomialZp.parse("1+2*b^3*c^3*d^3*e+2*a*b^2*c*d^2*e^3+a*b^3*c^2*d*e^2+a^3*b^2*c^3*d^2", domain, vars),
    }, base = arr[0].createOne().multiply(arr);

    lMultivariatePolynomialZp a = base;
    lMultivariatePolynomialZp b = a.derivative(1);
    
    for (int i = 0; i < 1000; i++) {
        timestamp();
        lMultivariatePolynomialZp gcd = ModularGCDFiniteField(a, b);
        timeElapsed();

        assertTrue(dividesQ(a, gcd));
        assertTrue(dividesQ(b, gcd));
    }
}

Possible solution is not to use cyclic (Vandermonde) substitutions.