# Optimal Constructions of Low-Hit Zone Frequency-Hopping Sequence Set Based on _m_-Sequence
## 4 Conclusions
** & **Parameters** & **Constraints** \\ \hline \multirow{4}{*}{[13]} & \((q(q^{n}-1),q|I|,q,Z,q^{n})\) & \(q^{n}-1=M(Z+1)\), \(M\
eq 1\) \\ \cline{2-3}  & \((q(q^{n}-1),q^{n}-1,q,q-1,q^{n})\) & - \\ \cline{2-3}  & \((s(q^{n}-1),M,q,Z,s(q^{n-1}-1))\) & \(q^{n}-1=M(Z+1)\),\(\gcd(s,q^{n}-1)=1\), \(s<M\) \\ \hline \multirow{4}{*}{[14]} & \((q^{n}-1,q^{k}(q-1),q^{k},\frac{q^{-1}-1}{q-1}-1,q^{n-k})\) & \(1\leq k\leq n\) \\ \cline{2-3}  & \((\frac{q^{n}-1}{l},q-1,q^{k},\frac{q^{-1}-1}{q-1},\frac{q^{-k}-1}{l})\) & \(1\leq k\leq n,t|(q-1),\gcd(t,n)=1\) \\ \hline \multirow{4}{*}{[15]} & \((q^{n}-1,q^{k}T,q^{k}L_{Z},q^{n-k})\) & \(q^{n}-1=T(L_{Z}+1),1\leq k\leq n\) \\ \cline{2-3}  & \((\frac{q^{n}-1}{l},T,q^{k},L_{Z},\frac{q^{-k}-1}{l})\) & \(q^{n}-1=T(L_{Z}+1),1\leq k\leq n\) \\ \hline \multirow{4}{*}{[16]} & \((T^{\frac{q^{n}-1}{l}},Ml,q,w-1,T\frac{q^{n-1}-1}{l})\) & \(l|(q^{n}-1)\), \(\frac{q^{n}-1}{l}=Mw\),\(\gcd(l,n)=1\), \(T=\lambda w+1\lambda\geq 1\), \(T<\frac{l(q^{n}-2)}{q-1}\) \\ \cline{2-3}  & \(l|(q^{n}-1)\), & \(2\leq r\leq l,\frac{r(q^{n}-1)}{l}=Mw\),\(\gcd(l,n)=1\) \\ \cline{2-3}  & \(T=\lambda w+1\lambda\geq 1\),\(T<\frac{l(q^{n}-2)}{q-1}\) \\ \cline{2-3}  & \((T(q^{n}-1),Mq^{k},q^{k},w-1,T(q^{n-k}-1))\) & \(1\leq k\leq n,q^{n}-1=Mw\), \(T=\lambda w+1\lambda\geq 1\),\(T<\frac{q^{n}(q^{n}-2)}{q-1}\) \\ \hline \multirow{4}{*}{[20]} & \((Tn,Ml,Q,w-1,TH_{m})\) & \(T\geq 2,Mw=n,T=\lambda w+1\) \\ \cline{2-3}  & \((p^{2}(q_{1}-1),pq_{1},p_{q1},\min\{p^{2}-1,q_{1}-1\}\) & \(\gcd(p^{2},q_{1}-1)=1,2p\leq q_{1}-1\) \\ \cline{2-3}  & \((p^{2}(q_{1}-1)(q_{2}-1),pq_{1}q_{2},\min\{p^{2}-1,q_{1}-2,q_{2}-\}\) & \(\gcd(p,q_{1}-1,q_{2}-1)=1,3p<\) \\ \cline{2-3}  & \((\frac{(q_{1}-1)-(q_{1}-1)}{d},q_{1}\cdots q_{k},q_{1}\cdots q_{k},q_{1}-1,1)\) & \(2<q_{1}<\cdots<q_{k},d=\gcd(q_{1},q_{2},\ldots,q_{k})\) \\ \cline{2-3}  & \((k_{1}k_{2}(q_{1}-1)(q_{2}-1),\frac{(q_{1}-1)(q_{2}-1)}{k_{1}k_{2}},\) & \(k_{1}|q_{1}-1,k_{2}|q_{2}-1,\gcd(k_{1}(q_{1}-1),k_{2}(q_{2}-1))=1\) \\ \cline{2-3}  & \(q_{1}q_{2},\min\{q_{1}-1,q_{2}-1\},k_{1}k_{2})\) & \(k_{1}(q_{1}-1)<k_{2}(q_{2}-1)\) and \(q_{1}>k_{1}k_{2}^{2}+2k_{1}k_{2}\) \\  & & or \(k_{1}(q_{1}-1)>k_{2}(q_{2}-1)\) and \(q_{2}>k_{2}k_{1}^{2}+2k_{1}k_{2}\) \\ \hline \multirow{4}{*}{[12]} & \(((q_{1}-1)(q_{2}^{n}-1),q_{1}q_{1}q_{2},q_{2}^{n}-2,q_{2}^{n-1}-\) & \(q_{1}>q_{2}^{n}\gcd(q_{1}-1,q_{2}^{n}-1)=1\) \\ \cline{2-3}  & \((p^{2}(p^{2}-1),p,p^{2},p^{2}-2,p(p-1))\) & \(\gcd(p^{2},p^{2}-1)=1\) \\ \hline \multirow{4}{*}{[21]} & \((l(p^{n}-1),e,e+1,p^{n}-2,lf)\) & \(p^{n}-1=ef,lf\ell^{2}=(fe^{2}-1)(e+1-lf)\) \\ \cline{2-3}  & \((l(p^{n}-1),e,e+1,\frac{p^{n}-1-m}{m},lf)\) & \(p^{n}-1=ef,lf\ell^{2}m<(fe^{2}-m)(e+1-lf)\) \\ \hline \multirow{4}{*}{[22]} & \((lp,\theta,\theta+1,p-1,l\beta)\) & \(p-1=\theta\beta\beta\theta p<(\theta p-1)(l+\theta+1-l\beta)\) \\ \cline{2-3}  & \((2p,\theta,\theta,p-1,2(\beta+1))\) & \(p-1=\theta\beta\), \(\beta\) is even \\ \hline \multirow{4}{*}{Theorem 1} & \((q^{n}-1,q^{k}\left\lfloor\frac{q^{n}-1}{L+1}\right\rfloor,q^{k},L_{Z},q^{n-k})\) & \(2\leq L_{z}\leq\lfloor\frac{q^{n}-1}{2}\rfloor-1\) \\ \hline \multirow{4}{*}{Theorem 2} & \((q^{n}-1,\left\lfloor\frac{q^{n}-1}{L+1}\right\rfloor,q^{n-k},L_{Z},q^{n-k}-1)\) & \(2\leq L_{z}\leq\lfloor\frac{q^{n}-1}{2}\rfloor-1\) \\ \hline \multirow{4}{*}{Theorem 3} & \((\frac{q^{n}-1}{d},\left\lfloor\frac{q^{n}-1}{d(L+1)}\right\rfloor d,q^{n-k},L_{Z}, \frac{q^{n-k}-1}{d})\) & \(2\leq L_{z}\leq\lfloor\frac{q^{n}-1}{2d}\rfloor-1,q^{i}\) is odd prime or \\ \cline{2-3}  & \(q\) is prime or prime power. \(p,q_{1},q_{2},\ldots,q_{k}\) are prime numbers. \(Q,k,k_{1},n,m,w,t,r,l,M,T,Z,\theta,\beta\) are positive integers.