Dobble http://images.math.cnrs.fr/Dobble-et-la-geometrie-finie.html

projective finite plane based on ℤ₇

one point per card, one line per symbol, two points per line, 7+1
lines per point

cards: 7² (point pairs) + 7 (parallel lines) + 1 (extra parallel, the
"vertical" one) (???)

-------

let's try ℤ₃p

(0,0) (1,0) (2,0) | (i,0)
(0,1) (1,1) (2,1) | (i,1)
(0,2) (1,2) (2,2) | (i,2)
------------------+
(0,i)

[a] x=0    (0,0) (0,1) (0,2) (0,i)
[b] x=1    (1,0) (1,1) (1,2) (0,i)
[c] x=2    (2,0) (2,1) (2,2) (0,i)
[d] y=0    (0,0) (1,0) (2,0) (i,0)
[e] y=1    (0,1) (1,1) (2,1) (i,0)
[f] y=2    (0,2) (1,2) (2,2) (i,0)
[g] x+y=0  (0,0) (1,2) (2,1) (i,1)
[h] x+y=1  (0,1) (1,0) (2,2) (i,1)
[i] x+y=2  (0,2) (1,1) (2,0) (i,1)
[j] x+2y=0 (0,0) (1,1) (2,2) (i,2)
[k] x+2y=1 (0,2) (1,0) (2,1) (i,2)
[l] x+2y=2 (0,1) (1,2) (2,0) (i,2)
[m] x+y=i  (i,0) (i,1) (i,2) (0,i)

13 lines=symbols, 13 point=cards

card  symbols
----- -------
(0,0) a  d  g  j
(0,1) a   e  h   l
(0,2) a    f  i k
(0,i) abc         m
(1,0)  b d   h  k
(1,1)  b  e   ij
(1,2)  b   fg    l
(2,0)   cd    i  l
(2,1)   c e g   k
(2,2)   c  f h j
(i,0)    def      m
(i,1)       ghi   m
(i,2)          jklm


in "my" order:

(i,2)          jklm
(i,1)       hgi   m
(i,0)    efd      m
(0,i) abc         m
(2,0)   c  d  i  l
(1,2)  b  f  g   l
(0,1) a  e  h    l
(2,1)   ce   g  k
(1,0)  b   dh   k
(0,2) a   f   i k
(2,2)   c f h  j
(1,1)  b e    ij
(0,0) a    d g j