Best Known (128, 136, s)-Nets in Base 2
(128, 136, 4195326)-Net over F2 — Constructive and digital
Digital (128, 136, 4195326)-net over F2, using
- t-expansion [i] based on digital (127, 136, 4195326)-net over F2, using
- net defined by OOA [i] based on linear OOA(2136, 4195326, F2, 9, 9) (dual of [(4195326, 9), 37757798, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2136, 4195326, F2, 8, 9) (dual of [(4195326, 8), 33562472, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(220, 1025, F2, 8, 4) (dual of [(1025, 8), 8180, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(220, 1025, F2, 4, 4) (dual of [(1025, 4), 4080, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(220, 1025, F2, 3, 4) (dual of [(1025, 3), 3055, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 20, 1025)-net over F2, using
- appending kth column [i] based on linear OOA(220, 1025, F2, 3, 4) (dual of [(1025, 3), 3055, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(220, 1025, F2, 4, 4) (dual of [(1025, 4), 4080, 5]-NRT-code), using
- linear OOA(2116, 4194301, F2, 8, 9) (dual of [(4194301, 8), 33554292, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2116, large, F2, 2, 9), using
- linear OOA(220, 1025, F2, 8, 4) (dual of [(1025, 8), 8180, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2136, 4195326, F2, 8, 9) (dual of [(4195326, 8), 33562472, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2136, 4195326, F2, 9, 9) (dual of [(4195326, 9), 37757798, 10]-NRT-code), using
(128, 136, large)-Net over F2 — Digital
Digital (128, 136, large)-net over F2, using
- 219 times duplication [i] based on digital (109, 117, large)-net over F2, using
- t-expansion [i] based on digital (108, 117, large)-net over F2, using
- net defined by OOA [i] based on linear OOA(2117, large, F2, 9, 9), using
- appending kth column [i] based on linear OOA(2117, large, F2, 8, 9), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2117, large, F2, 3, 9), using
- appending kth column [i] based on linear OOA(2117, large, F2, 8, 9), using
- net defined by OOA [i] based on linear OOA(2117, large, F2, 9, 9), using
- t-expansion [i] based on digital (108, 117, large)-net over F2, using
(128, 136, large)-Net in Base 2 — Upper bound on s
There is no (128, 136, large)-net in base 2, because
- 6 times m-reduction [i] would yield (128, 130, large)-net in base 2, but