Combinatorics problem

Consider a \(4\)-dimensional array \(R\). Any element of the array can be represented by \(R_{abcd}\) where \(a,b,c,d\) are any four (not necessarily distinct) integers from the set \(\{1,2,3…N\}\).

Given that,

i) \(R_{abcd}=-R_{abdc}\)

ii) \(R_{abcd}=-R_{bacd}\)

iii) \(R_{abcd}=R_{cdab}\)

iv) \(R_{abcd}+R_{adbc}+R_{acdb}=0\)

When \(N=15\), how many elements of \(R\) are independent?

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