Ruzsa’s genus-one problem

Infinite CRT-graph family from the N=350 construction. Under Z/378 ≅ Z/14 × Z/27, take A={(r,g(r)):r∈Z/14} with integer labels g=(0,3,-4,7,8,-1,8,7,-4,3,0,1,6,1), reduced mod 27. For every nontrivial base solution mod 14, g(a)+3g(b)-2g(c)-2g(d) is nonzero; this fixed labeling works for every q≥25 coprime to 14.