The only maximal affine Hadamard families stemming from the Fourier matrix $$F_{15} = \left[\begin{array}{lllllllllllllll} 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1& 1\\ 1& w& w^2& w^3& w^4& w^5& w^6& w^7& w^8& w^9& w^{10}& w^{11}& w^{12}& w^{13}& w^{14}\\ 1& w^2& w^4& w^6& w^8& w^{10}& w^{12}& w^{14}& w& w^3& w^5& w^7& w^9& w^{11}& w^{13}\\ 1& w^3& w^6& w^9& w^{12}& 1& w^3& w^6& w^9& w^{12}& 1& w^3& w^6& w^9& w^{12}\\ 1& w^4& w^8& w^{12}& w& w^5& w^9& w^{13}& w^2& w^6& w^{10}& w^{14}& w^3& w^7& w^{11}\\ 1& w^5& w^{10}& 1& w^5& w^{10}& 1& w^5& w^{10}& 1& w^5& w^{10}& 1& w^5& w^{10}\\ 1& w^6& w^{12}& w^3& w^9& 1& w^6& w^{12}& w^3& w^9& 1& w^6& w^{12}& w^3& w^9\\ 1& w^7& w^{14}& w^6& w^{13}& w^5& w^{12}& w^4& w^{11}& w^3& w^{10}& w^2& w^9& w& w^8\\ 1& w^8& w& w^9& w^2& w^{10}& w^3& w^{11}& w^4& w^{12}& w^5& w^{13}& w^6& w^{14}& w^7\\ 1& w^9& w^3& w^{12}& w^6& 1& w^9& w^3& w^{12}& w^6& 1& w^9& w^3& w^{12}& w^6\\ 1& w^{10}& w^5& 1& w^{10}& w^5& 1& w^{10}& w^5& 1& w^{10}& w^5& 1& w^{10}& w^5\\ 1& w^{11}& w^7& w^3& w^{14}& w^{10}& w^6& w^2& w^{13}& w^9& w^5& w& w^{12}& w^8& w^4\\ 1& w^{12}& w^9& w^6& w^3& 1& w^{12}& w^9& w^6& w^3& 1& w^{12}& w^9& w^6& w^3\\ 1& w^{13}& w^{11}& w^9& w^7& w^5& w^3& w& w^{14}& w^{12}& w^{10}& w^8& w^6& w^4& w^2\\ 1& w^{14}& w^{13}& w^{12}& w^{11}& w^{10}& w^9& w^8& w^7& w^6& w^5& w^4& w^3& w^2& w \end{array}\right] : \quad w=\exp(2\pi i/15)$$ are $$\begin{aligned} F_{15}^{(8)}(a,b,c,d,e,f,g,h) & = F_{15}\circ{\rm EXP}\left(i R_{F_{15}^{(8)}}(a,b,c,d,e,f,g,h)\right),\\ \left(F_{15}^{(8)}(a,b,c,d,e,f,g,h)\right)^{\rm T} & = F_{15}\circ{\rm EXP}\left(i \left(R_{F_{15}^{(8)}}(a,b,c,d,e,f,g,h)\right)^{\rm T}\right) \end{aligned}$$ with $$\begin{aligned} R_{F_{15}^{(8)}}& (a,b,c,d,e,f,g,h)=\\ & \left[\begin{array}{ccccccccccccccc} \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet\\ \bullet& a& b& c& d& \bullet& a& b& c& d& \bullet& a& b& c& d\\ \bullet& e& f& g& h& \bullet& e& f& g& h& \bullet& e& f& g& h\\ \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet\\ \bullet& a& b& c& d& \bullet& a& b& c& d& \bullet& a& b& c& d\\ \bullet& e& f& g& h& \bullet& e& f& g& h& \bullet& e& f& g& h\\ \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet\\ \bullet& a& b& c& d& \bullet& a& b& c& d& \bullet& a& b& c& d\\ \bullet& e& f& g& h& \bullet& e& f& g& h& \bullet& e& f& g& h\\ \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet\\ \bullet& a& b& c& d& \bullet& a& b& c& d& \bullet& a& b& c& d\\ \bullet& e& f& g& h& \bullet& e& f& g& h& \bullet& e& f& g& h\\ \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet& \bullet\\ \bullet& a& b& c& d& \bullet& a& b& c& d& \bullet& a& b& c& d\\ \bullet& e& f& g& h& \bullet& e& f& g& h& \bullet& e& f& g& h \end{array}\right]. \end{aligned}$$ The families $F_{15}^{(8)}$ and $\left(F_{15}^{(8)}\right)^{\rm T}$ are cognate families.