  One of the most intriguing problems, in $q$-analogs of designs, is the
existence question of an infinite family of $q$-analog of Steiner systems,
known also as $q$-Steiner systems, (spreads not included) in general, and the
existence question for the $q$-analog of the Fano plane, known also as the
$q$-Fano plane, in particular. These questions are in the front line of open
problems in block design. There was a common belief and a conjecture that such
structures do not exist. Only recently, $q$-Steiner systems were found for one
set of parameters. In this paper, a definition for the $q$-analog of the
residual design is presented. This new definition is different from previous
known definition, but its properties reflect better the $q$-analog properties.
The existence of a design with the parameters of the residual $q$-Steiner
system in general and the residual $q$-Fano plane in particular are examined.
We prove the existence of the residual $q$-Fano plane for all $q$, where $q$ is
a prime power. The constructed structure is just one step from a construction
of a $q$-Fano plane.
