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A $[t]$-trade is a pair $T=(T_+, T_-)$ of disjoint collections
of subsets (blocks) of a $v$-set $V$ such that for every $0\le i\le t$,
any $i$-subset of $V$ is included in the same number
of blocks of $T_+$ and of $T_-$. It follows that $|T_+| = |T_-|$ and this common value is called the volume of $T$.
If we restrict all the blocks to have the same size, we obtain the classical $t$-trades as a special case of
$[t]$-trades.
It is known that the minimum volume of a nonempty $[t]$-trade is $2^t$.
Simple $[t]$-trades (i.e., those with no repeated blocks) correspond to a Boolean function of degree at most $v-t-1$.
From the characterization of Kasami--Tokura of such functions with small number of ones,
it is known that any simple $[t]$-trade of volume at most $2\cdot2^t$ belongs to one of two
affine types, called Type\,(A) and Type\,(B) where Type\,(A) $[t]$-trades are known to exist. By considering the affine rank, we prove that
$[t]$-trades of Type\,(B) do not exist.
Further, we derive the spectrum of volumes of simple trades up to $2.5\cdot 2^t$,
extending the known result for volumes less than $2\cdot 2^t$.
We also give a characterization of ``small" $[t]$-trades for $t=1,2$. Finally, an algorithm to produce $[t]$-trades for specified $t$, $v$
is given. The result of the implementation of the algorithm for $t\le4$, $v\le7$ is reported.
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