The base sequence conjecture for BS(n+1,n)

Let $BS(m,n)$ denote four sequences $A,B,C,D$ of $71$ of lengths $m,m,n,n$ with zero combined non-periodic autocorrelation, and let $BS(n+1,n)$ be the corresponding case. Base sequence conjecture. There is a $BS(n+1,n)$ for all integers $n\ge 0$. This conjecture is stronger than the Hadamard conjecture; it has been verified for all $n\le 40$ and for all Golay numbers, but the general assertion remains open.