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I was reading the lecture notes from

I am a little bit confused how points on the lattice gets assigned by a unique index j given in the lecture as

$$j = \sum_{i = 0}^{D-1} n_{i} L^{i}$$

Can any one explain what does it means. It is even not equal to total lattice sites V.

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This is just a way to index the $L^D$ lattice points. It's equivalent to giving each lattice point $j=(n_0,n_1,...,n_{D-1})$ an index whose digits in base $L$ are $n_0,n_1,...,n_{D-1}$ (from least to most significant). – mjqxxxx Nov 2 '12 at 4:55

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