 let ${\mathcal{X}}_S=\bigcup_{i\in S}{{\mathcal{X}}_i}$. Then the optimal codelength $N_{q,opt}$ over ${\mathds{F}}_q$ for the $(m,n,{\mathcal{X}},\delta_s)$ BNSI problem satisfies, $$N_{q,opt} \geq |{\mathcal{X}}_S|+ \min\{0\delta _s,n-|{\mathcal{X}}_S|\}