Best Known (148, 148+9, s)-Nets in Base 2
(148, 148+9, 5242878)-Net over F2 — Constructive and digital
Digital (148, 157, 5242878)-net over F2, using
- 21 times duplication [i] based on digital (147, 156, 5242878)-net over F2, using
- net defined by OOA [i] based on linear OOA(2156, 5242878, F2, 9, 9) (dual of [(5242878, 9), 47185746, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2156, 5242878, F2, 8, 9) (dual of [(5242878, 8), 41942868, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(240, 1048577, F2, 8, 4) (dual of [(1048577, 8), 8388576, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(240, 1048577, F2, 4, 4) (dual of [(1048577, 4), 4194268, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(240, 1048577, F2, 3, 4) (dual of [(1048577, 3), 3145691, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (36, 40, 1048577)-net over F2, using
- appending kth column [i] based on linear OOA(240, 1048577, F2, 3, 4) (dual of [(1048577, 3), 3145691, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(240, 1048577, F2, 4, 4) (dual of [(1048577, 4), 4194268, 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(240, 1048577, F2, 8, 4) (dual of [(1048577, 8), 8388576, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2156, 5242878, F2, 8, 9) (dual of [(5242878, 8), 41942868, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2156, 5242878, F2, 9, 9) (dual of [(5242878, 9), 47185746, 10]-NRT-code), using
(148, 148+9, large)-Net over F2 — Digital
Digital (148, 157, large)-net over F2, using
- 25 times duplication [i] based on digital (143, 152, large)-net over F2, using
- t-expansion [i] based on digital (141, 152, large)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
- 4 times NRT-code embedding in larger space [i] based on linear OOA(2140, large, F2, 3, 11), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
- t-expansion [i] based on digital (141, 152, large)-net over F2, using
(148, 148+9, large)-Net in Base 2 — Upper bound on s
There is no (148, 157, large)-net in base 2, because
- 7 times m-reduction [i] would yield (148, 150, large)-net in base 2, but