I've thought of this solution, it requires coding and a somewhat elaborate technical setup, but also eliminates lots of waste, both in time and paper.
Have a webform / app where student can sign in with their name, school and teacher. Upon signing, the system gives the student a unique id.
Where the lecture is given, setup a free wifi from which students must log in with their unique id at the beginning and at the end of the lecture.
Attendance can then be checked in this way: students that attended are only those whose unique id is present at the beginning and at the end of the lecture, according to time stamps and wi-fi origin.
Students can still comunicate each other their unique id and forge their attendance, but you can setup incentives against cooperation: indeed, make credits transferable, so that if one student knows more than one id, s/he can rob other students and give the credits to him/her.