Hi LA,

Is there any difference between picking a pair of numbers as Key Numbers or using them as a Matrix Pair?

Does Matrix come into play only when there's more than one pair involved, or is there a difference between Matrix and Key pairs of numbers even if we're only dealing with one number pair?

Thanks!

## Key Numbers vs Matrix Pair

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### Re: Key Numbers vs Matrix Pair

Hi iWin, key numbers are any numbers that form a particular group and all of them must show up together. So, any set of key numbers will show up in every block of the constructed covering.

Matrix is a general construction technique that combines various sets of groups to form blocks.

If Group 1 = G11, G12, G13 (3 different numbers)

Group 2 = G21, G22, G23 (another 3 different numbers)

Group 3 = G31, G32, G33 (another 3 different numbers)

etc

and we want to produce the block

X1 X2 X3 X4 X5 X6

a typical matrix would pick one number from group 1 (whichever among G11, G12, G13) to fill position X1, another number from group 2 (G21, G22, G23) to fill position X2 etc till all the X positions of the block are filled (obviously more such groups will be needed or set different requested numbers i.e. 1-2 from each group). When we form another block, a different number may be picked from group 1, from group 2 etc. Overall all the numbers among all the groups are expected to be used but this is not necessary if the coverage requirement is fulfilled somehow without the use of some numbers, even if they appear in a group. The pick methodology formation to fill each individual position of the block (the X1, X2 etc positions) is what we call matrix. So, key and matrix are not really related, they refer to different things.

Matrix is a general construction technique that combines various sets of groups to form blocks.

If Group 1 = G11, G12, G13 (3 different numbers)

Group 2 = G21, G22, G23 (another 3 different numbers)

Group 3 = G31, G32, G33 (another 3 different numbers)

etc

and we want to produce the block

X1 X2 X3 X4 X5 X6

a typical matrix would pick one number from group 1 (whichever among G11, G12, G13) to fill position X1, another number from group 2 (G21, G22, G23) to fill position X2 etc till all the X positions of the block are filled (obviously more such groups will be needed or set different requested numbers i.e. 1-2 from each group). When we form another block, a different number may be picked from group 1, from group 2 etc. Overall all the numbers among all the groups are expected to be used but this is not necessary if the coverage requirement is fulfilled somehow without the use of some numbers, even if they appear in a group. The pick methodology formation to fill each individual position of the block (the X1, X2 etc positions) is what we call matrix. So, key and matrix are not really related, they refer to different things.

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