Combinatoric system which using in bookies "S3" system I am interested what type of combinatorics is using for following bookmakers system called "S3":


We have  N={1..8} events
We build express pairs C=8 like

[(1, 2, 4), (1, 3, 6), (1, 6, 8), (2, 3, 5),
 (2, 5, 8), (3, 7, 8), (4, 5, 7), (4, 6, 7)]


Each event repeats 3-times: 1 =>  (1, 2, 4), (1, 3, 6), (1, 6, 8)..

It's not permutation, combination... Please advice what is it?

I want as example generate in similar way 4 from 10 if this possible. After I'd like to predict the optimal way for building the `pairs'
This can be interpreted as an unusual error correcting code with a non-binary signal.

Essentially, you want the tuples to be very different, i.e. there are no two tuples that agree in two positions. That is also a simple strategy for producing such codes (the more interesting question is what (x,y) combination is best.)

Think of it this way: assuming you only know part of the tuple. Say the first is unknown: (?, 2, 4) then you want to be able still conclude the correct triple.

https://en.wikipedia.org/wiki/Forward_error_correction