Points on polynomial curves in small boxes modulo an integer

Given an integer q and a polynomial f∈Zq[X] of degree d with coefficients in the residue ring Zq=Z/qZ, we obtain new results concerning number solutions to congruences form y≡f(x)(modq), variables lying some cube B side length H. Our argument uses ideas Cilleruelo, Garaev, Ostafe Shparlinski which reduces problem Vinogradov mean value theorem lattice point counting problem. We treat differently, using transference principles from geometry numbers. also use variant main conjecture for Bourgain, Demeter Guth Wooley, allows one deal when run through rather sparse sets.