nt.number theory - Spacing of zeros of zeta function on the critical line

I believe $Lambda(k)$ is the lower bound that arises from assuming the $k$th moment is predicted by random matrix theory (equation (1.13)) with the explicit constants $b(h,k)$ derived by Hughes. The method seems to require knowledge of the constants $b(k,k)$. Indeed at the top of page 5 he discusses the work of Hall in the case $h=3$, for which the value of $Lambda$ derived (equation (1.17)) occurs in the table (1.18) as $Lambda(3)$.