A unimodular lattice is an integral lattice whose Gram matrix has determinant 
or 
(Milnor and Husemoller 1973). Thus the lattice equals its
dual under the defining bilinear form. A positive
definite unimodular point lattice has covolume
1.
Kubischta (2026, pp. 2-3) constructed a positive definite unimodular lattice of rank 37 with minimum squared Euclidean norm
4 and kissing number 35594. A 4-frame in this lattice
consists of 37 mutually orthogonal vectors
of squared Euclidean norm 4. It gives a Type I
self-dual code over 
of length 37 and minimum Euclidean weight 16. Kubischta reports using ChatGPT in
the search for candidate lattices and the exploration of constructions. The paper
lists orbit representatives for the 4-frame.
