16 teams, 8 events, 8 time periods.

[spector17]

I don't believe it is possible at the moment for the ideal of 16 teams, 8 events and 8 times.  It may be possible for 16 teams, 9 events, 9 times.

Rules in order of importance:

1) Each team plays each event once.
2) Two teams do not play each other more than once.
3) There must be 16 teams.
3) There must be 8 events and 8 times.

Much thanks!

[Ian Wakeling]

Both of these are possible.  For example 8x8:

(P O) (L A) (N D) (B F) (C J) (I G) (M E) (K H)
(L G) (P E) (B J) (N H) (K D) (M O) (I A) (C F)
(K E) (C G) (M H) (I J) (L F) (B A) (N O) (P D)
(C A) (K O) (I F) (M D) (P H) (N E) (B G) (L J)
(I H) (M J) (C E) (K G) (N A) (P F) (L D) (B O)
(M F) (I D) (K A) (C O) (B E) (L H) (P J) (N G)
(B D) (N F) (L O) (P A) (M G) (K J) (C H) (I E)
(N J) (B H) (P G) (L E) (I O) (C D) (K F) (M A)

and 9x9:

(L A) (O B) (P M) (K F) (E N) (---) (C I) (D H) (J G)
(P J) (G L) (C E) (B I) (M K) (D A) (H F) (O N) (---)
(D M) (---) (L K) (J C) (I H) (B N) (O G) (F A) (P E)
(---) (J F) (B A) (P O) (L C) (M H) (K N) (G E) (D I)
(C N) (D K) (J I) (L H) (G A) (O E) (---) (P B) (M F)
(I K) (P N) (G H) (D E) (J O) (C F) (M A) (---) (L B)
(B E) (I A) (O F) (G M) (---) (J L) (P D) (C K) (H N)
(G F) (C H) (---) (N A) (D B) (P I) (L E) (J M) (O K)
(O H) (M E) (D N) (---) (P F) (G K) (J B) (L I) (C A)

They are symmetric in the sense that rows could be rounds and columns events, or vice-versa.

[ynwvalk99]

Is it possible for this to extend to a total of 3 days?  I know at that point some teams will play each other twice but would like to minimize that as well as ensure they at least do not play each other twice in the same event.  

Thanks,

[Ian Wakeling]

Extending to multiple days will be difficult.  For 16 teams and 8x8, then you could use this schedule to give 2 days.  The first 8 rows of the 15x8 schedule are equivalent to the 8x8 schedule above, so use this for day 1.  Now rotate all columns (events) of the schedule along a position, so column 1 is moved to the right becoming column 2, etc., and the 8th column is moved back to become the new column 1.  Then on day 2 play rows 8 to 15 of the shifted schedule.  Notice that row 8 is used twice, so play this round 1st on day 1 and last on day 2.

Hope that helps.