Best Known (56−7, 56, s)-Nets in Base 2
(56−7, 56, 262142)-Net over F2 — Constructive and digital
Digital (49, 56, 262142)-net over F2, using
- net defined by OOA [i] based on linear OOA(256, 262142, F2, 7, 7) (dual of [(262142, 7), 1834938, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(256, 262143, F2, 3, 7) (dual of [(262143, 3), 786373, 8]-NRT-code), using
(56−7, 56, 262143)-Net over F2 — Digital
Digital (49, 56, 262143)-net over F2, using
- net defined by OOA [i] based on linear OOA(256, 262143, F2, 7, 7) (dual of [(262143, 7), 1834945, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(256, 262143, F2, 6, 7) (dual of [(262143, 6), 1572802, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(256, 262143, F2, 3, 7) (dual of [(262143, 3), 786373, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(256, 262143, F2, 6, 7) (dual of [(262143, 6), 1572802, 8]-NRT-code), using
(56−7, 56, 600155)-Net in Base 2 — Upper bound on s
There is no (49, 56, 600156)-net in base 2, because
- 1 times m-reduction [i] would yield (49, 55, 600156)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 36028 807678 782163 > 255 [i]