With 11 players and 3 byes per round, it is probably best to go for 11 rounds, so that each player gets exactly 8 games and three bye rounds. It's possible to arrange this, so each player has 8 different partners and sees all other players as opponents either once or twice. Below the byes are nicely separated, with at least two rounds of play between between byes.
11 players & 11 rounds:
(I G v E J) (B F v K C) (D H A)
(J H v F K) (C G v A D) (E I B)
(K I v G A) (D H v B E) (F J C)
(A J v H B) (E I v C F) (G K D)
(B K v I C) (F J v D G) (H A E)
(C A v J D) (G K v E H) (I B F)
(D B v K E) (H A v F I) (J C G)
(E C v A F) (I B v G J) (K D H)
(F D v B G) (J C v H K) (A E I)
(G E v C H) (K D v I A) (B F J)
(H F v D I) (A E v J B) (C G K)
With 15 players, any multiple of 5 rounds would be a sensible choice. Below I give an example with 15 rounds, where each player has 12 games, 12 different partners and, all other players as opponents either once or twice. Players have one bye in the first 5 rounds, one bye in rounds 6 to 10, and one bye in the last five rounds.
(B G v E I) (A M v F J) (K O v L D) (C H N)
(C H v A J) (B N v G F) (L K v M E) (D I O)
(D I v B F) (C O v H G) (M L v N A) (E J K)
(E J v C G) (D K v I H) (N M v O B) (A F L)
(A F v D H) (E L v J I) (O N v K C) (B G M)
(O L v A I) (B D v J N) (M F v E G) (C H K)
(K M v B J) (C E v F O) (N G v A H) (D I L)
(L N v C F) (D A v G K) (O H v B I) (E J M)
(M O v D G) (E B v H L) (K I v C J) (A F N)
(N K v E H) (A C v I M) (L J v D F) (B G O)
(H N v D M) (O E v A B) (G I v K F) (L J C)
(I O v E N) (K A v B C) (H J v L G) (M F D)
(J K v A O) (L B v C D) (I F v M H) (N G E)
(F L v B K) (M C v D E) (J G v N I) (O H A)
(G M v C L) (N D v E A) (F H v O J) (K I B)
I hope your Euchre group finds these schedules useful.
Ian.
For the benefit of other readers here are some links to other schedules on this message board relating to doubles play:
7 players 7 rounds10 players 10 rounds10 players 15 rounds14 players 14 rounds18 players 18 rounds20 players 10 rounds22 players 22 rounds24 players 10 rounds24 players 12 roundsFor fully balanced schedules involving 4n players then click on the schedules link near the top of this page and select "Whist" and the number of players to display a suitable schedule.