20 teams - 4 Byes per Week (with a twist)

[tjb3]

Ok maybe here is a new one:
20 Teams - Team Captains are assigned to each Team and stay with each Team.  The Captain is assigned 5 different Players each week.  To complicate the matter, only 16 Teams will compete each week so to have each Team receive the same number of byes the League will go for 20 weeks.  This is a truncated League and not every Team pairing will occur.  Additionally, each individual Player must participate in the same number of Byes, including the Team Captains.  
Can a schedule be created for this?

[Ian Wakeling]

I can't see any way to do this.  Even taking the team captains out of the equation and considering it as 8 games of 5 against 5 each week, then I still can't come close to balancing pairs of players and byes.

[tjb3]

OK, Thanks for looking into this.