THE CONSTRUCTION OF INFINITE FAMILIES OF k-TIGHT OPTIMAL DOUBLE LOOP NETWORKS
任意k紧优双环网络无限族的构造

Based on the theory of $L$-shaped tile, Chinese remainder theorem and prime number theory, it is proved that infinite families of $k_0$-tight optimal double loop networks can be constructed when $A+z-2j\ne0$, $\{N(t)=3t^{2}+(2i-1)t+B$; $B=k_0^2-nk_0+m, t=f^2-if-nk_0+m$, $f=(2i-i^2+4B)p_1^2 p_2^2\cdotsp^2_{k_0^2}e+c$, where $i=1,3, e\ge0, m,n$ are integers\}. The number $N(t)$ of nodes can be a polynomial of degree 4 in $e$ or a polynomial of degree 2 in $e$ with integral coefficients containing a parameter.