# Order 19

## The three inequivalent saturated D-optimal designs of order 19

There are exactly three Hadamard equivalence classes of saturated
D-optimal designs (that is to say, maximal determinant {+1,-1} matrices) of
order 19.

They are:
R1,
R2,
R3.
The maximal determinant for order 19 is
833*4^6*2^18 = 3411968*2^18 = 894426939392
(97.5% of the Ehlich bound).

As discussed in our paper, R1 gives one Gram matrix G1 = R1.R1^T;

R2 and R3 give a different Gram matrix G2 = R2.R2^T = R3.R3^T.

## Candidate Gram matrices

As discussed in our paper, the proof that R1, R2 and R3 above are the
(unique, up to Hadamard equivalence) D-optimal designs of order 19
depends on testing nine candidate Gram matrices. These are given
here in compressed format (one matrix per line).