On the (Fourier analytic) Sidon constant of {0,1,2,3}

This constant is the maximum of the sum $\mathrm{\mid }{c}_0\mathrm{\mid }+\mathrm{\mid }{c}_1\mathrm{\mid }+\mathrm{\mid }{c}_2\mathrm{\mid }+\mathrm{\mid }{c}_3\mathrm{\mid }$ of the moduli of the coefficients of a trigonometric polynomial $c_0+c_1{e}^{it}+c_2{e}^{2it}+c_3{e}^{3it}$ bounded by 1. Its value is still unknown, but I will present some ideas on how to compute it and describe a distinguished torus of extremal functions.