  The design of modulation schemes for the physical layer network-coded two way
relaying scenario is considered with the protocol which employs two phases:
Multiple access (MA) Phase and Broadcast (BC) Phase. It was observed by
Koike-Akino et al. that adaptively changing the network coding map used at the
relay according to the channel conditions greatly reduces the impact of
multiple access interference which occurs at the relay during the MA Phase and
all these network coding maps should satisfy a requirement called the {\it
exclusive law}. We highlight the issues associated with the scheme proposed by
Koike-Akino et al. and propose a scheme which solves these issues. We show that
every network coding map that satisfies the exclusive law is representable by a
Latin Square and conversely, and this relationship can be used to get the
network coding maps satisfying the exclusive law. Using the structural
properties of the Latin Squares for a given set of parameters, the problem of
finding all the required maps is reduced to finding a small set of maps for
$M-$PSK constellations. This is achieved using the notions of isotopic and
transposed Latin Squares. Even though, the completability of partially filled
$M \times M$ Latin Square using $M$ symbols is an open problem, two specific
cases where such a completion is always possible are identified and explicit
construction procedures are provided. The Latin Squares constructed using the
first procedure, helps towards reducing the total number of network coding maps
used. The second procedure helps in the construction of certain Latin Squares
for $M$-PSK signal set from the Latin squares obtained for $M/2$-PSK signal
set.
