  3-phase Golay sequence and array triads are a natural generalisation of
2-phase Golay sequence pairs, yet their study has until now been largely
neglected. We present exhaustive search results for 3-phase Golay sequence
triads for all lengths up to 24, showing that the existence pattern is much
richer than that for 2-phase Golay sequence pairs. We give an elementary proof
that there is no 3-phase Golay sequence triad whose length is congruent to 4
modulo 6. We give two construction methods for 3-phase Golay array triads, and
show how to project 3-phase Golay array triads to lower-dimensional Golay
triads. In this way we explain much of the existence pattern found by
exhaustive search.

Combinatorics