New lower bounds for binary constant-weight codes from prescribed-automorphism search, and two quantum codes meeting their upper bounds

We give explicit binary constant-weight codes that raise the lower bounds on $A(n,6,w)$ in eight cells of Brouwer's table, all now listed there. The first round (9 October 2026) gave four values: $A(27,6,11)\ge 19305$, $A(27,6,12)\ge 24453$, $A(28,6,10)\ge 18642$ and $A(28,6,9)\ge 11154$, together w