9.4 $G(2,4) \vert E$

Besides the method used to compute cosets the ordering plays an important role. Example $G(2,4) \vert E$ was computed using 669 different orderings. The maximal/total number of cosets computed varied from 1728/1756 to 13560/14941 using method (4). Even for orderings which seemed to be ''similar'' the number of cosets was quite different. Table shows the maximal and the total number of cosets for example $G(2,4) \vert E$ using a Knuth-Bendix ordering with the respective weights attached to the letters of the alphabet.

Table: Example $G(2,4) \vert E$ using different orderings

a	b	A	B	$max\{N\}$	$\vert N\vert$
1	5	4	1	3074	3111
1	5	4	2	3313	3331
1	5	4	3	3421	3430
1	5	4	4	8901	8952
1	5	4	5	3432	3439