Some experimental results on the Frobenius problem

We study the Frobenius problem: given relatively prime positive integers $a_1,\mathrm{.}\mathrm{.}\mathrm{.},a_d$, find the largest value of t (the Frobenius number) such that ${\sum }_{k=1}^d{m}_k{a}_k=t$ has no solution in nonnegative integers $m_1,\mathrm{.}\mathrm{.}\mathrm{.},m_d$. Based on empirical data, we conjecture that except for some special cases the Frobenius number can be bounded from above by $\sqrt{a_1 a_2 a_3}^{5/4} - a_1 - a_2 - a_3$.