Ratio of |Det R_{j}| to Ehlich/Wojtas bound: 1

M=R_{j}^{T}R_{j}=
R_{j} R_{j}^{T} for j=1, 2 , ..., 8:

| S 0 | M = | | | 0 S |with S = 36 I + 2 J where I is the 19×19 identity matrix and J is the 19×19 matrix with all entries 1.

There are eight inequivalent matrices composed of circulant blocks, A and
B:

| A B | | | | T T| |-B A |The first rows of A and B are:

R

+++++---+-++-++++-+ +++--+--+++-+-+++-+R

+++++---+-++-++++-+ ++++--+++-+-+--++-+R

++++++---+-+-++++-+ +++--+++-++-++--+-+R

++++++-++-++--+-+-+ +++++---++-+-+++--+R

++++++---++-++-++-+ +++++--+++--+-+-+-+R

+++++++-+--+++--+-+ +++--+--+++-+-+++-+R

+++++++-+--+++--+-+ ++++--+++-+-+--++-+R

++++++++--++-+-+--+ +++--+-+++-+--+++-+

Notes:

- A maximal determinant was first reported by Ehlich [E1].
- The complete set of circulant block forms was found by Yang [Y3]. That there are eight inequivalent ones was shown by Kounias, Koukouvinos, Nikolaou and Kakos [KKNK1] who gave the forms listed here.
- Are there other inequivalent matrices not in the form of circulant blocks?

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This page created 10 March 2002.