  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.
