2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76192The aim of this paper is to present a construction of smooth rational surfaces in projective fourspace with degree 12 and sectional genus 13. The construction is based on exterior algebra methods, finite field searches and standard deformation theory.13 pages. Singular or Macaulay2 scripts needed to construct and analyse these surfaces are available at http://www.math.uni-sb.de/~ag-schreyer and http://www.math.colostate.edu/~abo/programs.htmlAlgebraic Geometry14J10, 14J26; 14Q10text