On his debut in the 2016 Grand Prix , he won his first point straight away in Oberwiesenthal . After he reached the points in Oberstdorf , he finished 42nd in the summer ranking. Vytrval was appointed to the Czech squad for the first time for the World Cup weekend in Lillehammer in early December 2016 . In the 4 × 5 km relay competition from Lysgårdsbakken , he was seventh together with Miroslav Dvořák , Tomáš Portyk and Ondřej Pažout. Two days later, he clearly missed the points in his first Gundersen individual in the World Cup. The 2017 Junior World Championships in Park Ciy were more successful with winning the bronze medal in the team competition together with Ondřej Pažout, David Zemek and Lukáš Daněk . In the Gundersen Singles he was twelfth, in the sprint it was enough for 16th place. In his only appearance in the 2016/17 Continental Cup in Eisenerz , he placed in the top thirty both times. Despite these streaky performance was Vytrval part of the Czech team at the Nordic World Ski Championships 2017 in Finland's Lahti . There he finished eleventh in the team with Miroslav Dvořák, Tomáš Portyk and Ondřej Pažout and reached 48th place in the Gundersen competition on the normal hill. He was not nominated for the other two title fights.
He completed his strongest Junior World Ski Championships in 2018 in Kandersteg , where he won the bronze medal in individual over the sprint distance behind Vid Vrhovnik and Dominik Terzer . Before that, he was fifth in the Gundersen singles over ten kilometers and fourth in the relay. He confirmed this performance a week later in the Continental Cup , when he was able to achieve his first top 10 placements in the Continental Cup in Eisenerz as tenth and fifth. At the end of the season in March, he therefore took part in the competitions of the last four World Cup stations, but was unable to collect any World Cup points. He achieved this for the first time on December 23, 2018 in Ramsau . With further points in Val di Fiemme , he finished 63rd in the overall World Cup ranking 2018/19 . At the Nordic World Ski Championships 2019 in Seefeld , Vytrval only took the lower ranks in the individual competitions. He also lagged far behind the leaders in the team sprint as tenth and ninth in the relay.
With good results in the 2019 Grand Prix , including tenth in the final competition in Planica , Vytrval was able to draw attention to himself. His good summer was reflected in the overall ranking with 18th place and 84 points. Nevertheless, he did not start the winter until mid-December at the Continental Cup competition in Park City.