Determine the minimal numbers of generators for the level-2 twist subgroup

Determine the minimal numbers of ordinary generators and involution generators, denoted respectively by m(T_2(N_g)) and im(T_2(N_g)), for the level-2 twist subgroup T_2(N_g) of the mapping class group of the non-orientable closed surface N_g, for every genus g≥4.

Background

The paper studies T_2(N_g)=M_2(N_g)∩T(N_g), where M_2(N_g) is the subgroup of the mapping class group acting trivially on H_1(N_g;Z_2), and T(N_g) is the subgroup generated by Dehn twists. It establishes generating sets for T_2(N_g) of cardinality (g−1)^2+\binom{g−1}{3}+1, including an involution generating set for sufficiently large genus.

Known lower and upper bounds leave the exact minimal generator numbers unresolved. In particular, the paper gives bounds differing by two for the ordinary and involution generating numbers in the relevant genus ranges, and also records partial bounds for genera 3 and 4. The stated problem asks for the exact values for all g≥4.