Log24

(Continued)

From the abstract of a talk, "Extremal Lattices," at TU Graz
on Friday, Jan. 11, 2013, by Prof. Dr. Gabriele Nebe
(RWTH Aachen) —

"I will give a construction of the extremal even
unimodular lattice Γ of dimension 72  I discovered
in summer 2010. The existence of such a lattice
was a longstanding open problem. The
construction that allows to obtain the
minimum by computer is similar to the one of the
Leech lattice from E₈ and of the Golay code from
the Hamming code (Turyn 1967)."

On an earlier talk by Nebe at Oberwolfach in 2011 —

"Exciting new developments were presented by
Gabriele Nebe (Extremal lattices and codes ) who
sketched the construction of her recently found
extremal lattice in 72 dimensions…."

Nebe's Oberwolfach slides include one on 
"The history of Turyn's construction" —

Nebe's list omits the year 1976. This was the year of
publication for "A New Combinatorial Approach to M₂₄"
by R. T. Curtis, the paper that defined Curtis's 
"Miracle Octad Generator."

Turyn's 1967 construction, uncredited by Curtis, may have
been the basis for Curtis's octad-generator construction.

See Turyn in this journal.